%%%
%%% Trame pour le rapport d'activité 2012
%%% --------------------------------------

%%%
%%% La chaine ``'' se trouve \`a la fin des lignes qui doivent etre obligatoirement modifiées ou supprimées. 
%%% Il de doit donc plus en rester aucune lors du dépot.

%%% Source : http://irabot.inria.fr/skel?projet=modemic
%%%
%%% Ce document est un squelette de rapport d'activité 
%%% mis \`a jour \`a partir des bases de données de l'INRIA
%%% (HAL pour les publis, BASTRI pour les équipes, l'entrepôt pour les données DRI et DPE ...).
%%% Le rédacteur peut compléter ce document et adapter la bibliographie. 
%%%
%%% Récuperer l'archive tgz de 2012 et la décompresser 
%%% dans un répertoire. Il y a un fichier tex et 3 fichiers de bibliographie (.bib) : 
%%% - modemic2012.tex : le texte en latex du rapport 
%%% - modemic2012.bib : les publis de l'année 2012 issues de Hal
%%% - modemic_refer2012.bib : les publications de référence (c'est-a-dire les publis les plus importantes
%%%   de l'équipe quelle que soit l'année)
%%% - modemic_foot2011.bib : les publis placées dans les notes de bas de page 
%%%  (footnote) issues de votre rapport 2011
%%%
%%% Instructions pour l'écriture du RA :
%%% http://www.inria.fr/interne/disc/publier/raweb.html
%%%
%%% Pour compiler le rapport utiliser le serveur iRAbot : 
%%% http://irabot.inria.fr/irabot
%%% ou bien le script irabot.sh qui utilise iRAbot.
%%% Certains centres ont leur propre serveur de compilation.
%%%
%%% Le rapport est en ANGLAIS
%%%

\documentclass{ra2012}

%SKEL - v0.4 - 2012 (Utiliser pour les stats d'utilisation de Skel, merci de ne effacer cette ligne)
% ne pas enlever 
\renewenvironment{motscle}{\begin{xmlelement}{keywords}}{\end{xmlelement}}

%%% Par defaut sont inclus les packages : html, french, graphics et footbib 
%%% (ifthen curves soul epsf html)
%%% Le plus souvent la commande \usepackage n'est pas prise en compte 
%%% Mais si le package est calc ou fp certaines commandes sont rendues disponibles
%%% (fancyvrb) 

%%% Mettez ici les \newcommand et \def que vous voulez



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
%%%  Information sur les données importées : Bastri
%%%
%%% Les organismes ou écoles partenaires de votre équipe ainsi que les labos auxquels
%%% vous êtes associés seront affichés automatiquement et \`a postériori, comme vos CRI, 
%%% thème et domaine de rattachement. Ces infos sont issues de Bastri : 
%%% https://bastri.inria.fr, la base des structures de recherche INRIA.
%%%
%%% L'acronyme de votre équipe sera également présenté comme dans les fiches projets.
%%% Si vous souhaitez le modifier, faites-le dans la base de gestion des fiches projets :
%%% https://bastri.inria.fr/FichesProjets/ et régénérez votre trame.
%%%
%%% Le "moreinfo" de l'équipe servira donc uniquement \`a préciser la localisation 
%%% quand elle est distincte du CRI (pour ceux qui le souhaitent).  
%%% 
%%% Vérifiez et signalez erreurs et problèmes : raweb-support@inria.fr
%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%% \projet{<PROJET>}{<ALT-ABRE>}{<NOM-PROJET-EXPLICITE>}
%%% exemple : 
%%% \projet{EXEMPLE}{ExemplE}{Algebraic Systems for Research and Industry} 
%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Informations concernant l'equipe extraites de BASTRI
% Source : http://bastri.inria.fr/
% Date : mardi 4 décembre 2012, 21:52:22 (UTC+0100)
%

\projet{MODEMIC}{modemic}{Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organismes}

%% Pour information le domaine et le theme du projet 
%% Domaine : Computational Sciences for Biology, Medicine and the Environment
%% Theme : Observation, Modeling, and Control for Life Sciences


%%% Type de groupe  
%%% EPI - équipe - action exploratoire
%%% Utilisez oui si EPI, non si équipe ou bien AE pour action exploratoire
%%% oui - non - AE

\isproject{oui}


%%% CRI INRIA 
%%% Sophia, ou Rocquencourt, ou Nancy, si le projet est bilocalisé : \UR{cr1,cr2} etc

\UR{Sophia}


%%% Des mots-clés décrivant l'activité de votre équipe ont été pré-remplis. 
%%% Pour les CR de Rennes, Bordeaux et Grenoble, les mots-clés pré-remplis sont ceux issus de la mise \`a jour faite en CP.
%%% Pour les autres, sont exportés les mots-clés du RA 2011.
%%% http://intranet.inria.fr/disc/publier/raweb2012instructions#Motscles


\begin{motscle}
Models; 
Microbial Ecology; 
Control Theory; 
Population Modeling; 
Multiscale Models; 
Individual-based Models.
\end{motscle}


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\begin{document}
\maketitle
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%%% Attention, il n'y a plus de \nocite{*} par defaut. 
%%% Vous pouvez mettre des \nocite{xx}, ou meme un \nocite{*}

%\nocite{TFE98}
%\nocite{AGATHISC}
%\nocite{FD98}
%\nocite{x,y,z} 

%%% Pour ceux qui le souhaitent le moreinfo permet d'insérer un texte
%%% de 3 - 4 lignes qui indique les particularités de l'équipe
%%% Il permet par exemple de préciser la localisation quand elle est distincte du CRI. 
%%% Ne doublonnez pas thème, domaine, CRI et partenariats qui sont ajoutés automatiquement. 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{moreinfo}
MODEMIC is a common INRA-INRIA team that aims at sharing skills of researchers of both Institutes for developing, analysing and simulating new models of microbial ecosystems as efficient tools to understand, explore, pilot and manage industrial and
natural bioprocesses. MODEMIC is located on the Montpellier SupAgro campus and it is housed by the UMR INRA-SupAgro MISTEA (Mathematics, Informatics and STatistics for Environment and Agronomy).
\end{moreinfo}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
%%% Liste des modules possibles pour les sections :
%%% presentation* fondements domaine logiciels
%%% resultats contrats* partenariat* diffusion*
%%% Seule la section presentation est obligatoire.
%%%
%%% ex : \begin{module}{composition}
%%%
%%% \begin{module} {<SECTION>} {<NOMMODULE>} {<TITRE>}
%%%     <PERSONNES> 
%%%    [<GLOSSAIRE>] 
%%%    [<MOREINFO>] 
%%%    [<RESUME>]  
%%%    <CORPS>
%%% \end{module}
%%%
%%%
%%% NOMMODULE est un identifiant unique pour reperer le module,
%%% aussi chaque module doit en avoir un NOMMODULE different  
%%%
%%% \begin{module}{logiciels}{calcul-formel}{Sofrware aspects of Computer Algebra}
%%%  \begin{participants}
%%%  format: \pers <PRENOM> [<PARTICULE>] <NOM> [<MOREINFO>]
%%%        \pers{Jean}[de]{La Fontaine}[1621-1695],
%%%        \pers{Cecil Blount}{De Mille}
%%%  \end{participants}
%%%  \begin{glossaire}
%%%       \glo{backward combatability}{A property of hardware or software
%%%   ... but activeliy... }
%%%  \end{glossaire}
%%%  \begin{abstract}
%%%       Le joli résumé que voil\`a
%%%  \end{abstact} 
%%%  This is a very short module with a hypertext link to the
%%%  \href{http://www.eps.mcgill.ca/jargon/jargon.html}{Jargon File}.
%%% \end{module}
%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
%%% Composition de l'equipe
%%%
%%% Professions possibles :
%%% Visiteur Chercheur Enseignant Technique Assistant
%%% PhD PostDoc AutreCategorie
%%% 
%%% Affiliations possibles :    
%%% INRIA CNRS AutreEtablissementPublic UnivFr 
%%% UnivEtrangere EtablissementPrive AutreAffiliation
%%% 
%%% Utiliser le mot-clé [Habilite] pour les titulaires d'une Thèse d'état ou d'une HDR
%%%
%%% Vérifier si les noms sonts corrects 
%%%
%%%       \pers{Prénom}{Nom}{profession}{affiliation}[champ_libre: grade, date][Habilite]?
%%%        ...
%%%
%%% La mention "Team leader" est précisée dans le champ libre (moreinfo)
%%%
%%% Dans ce champ libre, si vous indiquez le grade, écrivez :
%%%      Senior Researcher  pour DR, 
%%%      Researcher pour CR , 
%%%      Professor, 
%%%      Associate Professor pour Maître de conf.
%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
%%% Information sur les données importées : membres de l'équipe
%%% 
%%% Le RAweb 2011 est utilisé pour récupérer les membres permanents 
%%% de l'équipe (c'est \`a dire sans les visiteurs, les postDoc et les divers).
%%% 
%%% Url de consulation du RAweb 2011 : http://raweb.inria.fr/rapportsactivite/RA2011/modemic/uid0.html
%%% En cas de problème avec le RAweb 2011 : raweb-support@inria.fr
%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

 %%% http://intranet.inria.fr/disc/publier/raweb2012instructions.html#modulemembers
 %%% L'exemple ne s'applique pas aux projets multi-localisés, qui ajouteront le CRI de rattachement après chaque nom entre [].



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% composition
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%---------------------------------------------------------------------
% Liste du personnel construite d'apres les informations du RAweb 2011
% Cette liste doit être mise \`a jour car elle ne contient que les permanents 2011
% Source : http://ralyx.inria.fr/Raweb/modemic/uid1.html
% Date : mardi 4 décembre 2012, 21:52:22 (UTC+0100)
%---------------------------------------------------------------------

\begin{composition}

% --- permanents
\pers{Fabien}{Campillo}{Chercheur}{INRIA}
     [Senior Researcher, INRIA Sophia-Antipolis]
     [Habilite]
\pers{C\'eline}{Casenave}{Chercheur}{AutreEtablissementPublic}
     [Junior Researcher, since September 2011, INRA]
\pers{Bart}{Haegeman}{Chercheur}{INRIA}
     [Junior Researcher, INRIA Sophia-Antipolis, on secondment
     to CNRS, since September 2012]
\pers{J\'er\^ome}{Harmand}{Chercheur}{AutreEtablissementPublic}
     [Senior Researcher, INRA Narbonne]
     [Habilite]
\pers{Geneviève}{Carrière}{Assistant}{INRIA}
     [AI, part time]
\pers{Alain}{Rapaport}{Chercheur}{AutreEtablissementPublic}
  [Team leader; Senior Researcher, INRA Montpellier]
   [Habilite]

% --- Enseignants
\pers{Térence}{Bayen}{Enseignant}{UnivFr}
     [Associate Professor, Universit\'e de Montpellier II; 
      ``d\'el\'egation'' INRIA since September]
\pers{Marc}{Joannides}{Enseignant}{UnivFr}
     [Associate Professor, Universit\'e de Montpellier II]
\pers{Claude}{Lobry}{Enseignant}{UnivFr}
     [Professor emeritus, Universit\'e de Nice][Habilite]
\pers{Tewfik}{Sari}{Enseignant}{UnivFr}
     [Professor, Universit\'e de Haute-Alsace; 
     Senior Researcher Irstea Montpellier][Habilite]

% --- collaborateurs exterieurs
\pers{Guillaume}{Deffuant}{CollaborateurExterieur}{AutreEtablissementPublic}[Senior Researcher, Irstea Clermont][Habilite]
\pers{Annick}{Lesne}{CollaborateurExterieur}{CNRS}
     [Senior Researcher, LPTMC Paris Jussieu][Habilite]
\pers{Antoine}{Rousseau}{CollaborateurExterieur}{INRIA}
     [Junior Researcher, MOISE Team-Project, INRIA-Rh\^one-Alpes]
% --- post-doc
\pers{Chlo\'e}{Deygout}{PostDoc}{AutreEtablissementPublic}
   [ANR DISCO grant, January and February]
\pers{Matthieu}{Sebbah}{PostDoc}{AutreEtablissementPublic}
     [INRIA-CIRIC grant, since October]
% --- doc
\pers{Walid}{Bouhafs}{PhD}{UnivEtrangere}
     [Université Tunis Carthage grant]
\pers{Boumediene}{Benyahia}{PhD}{AutreEtablissementPublic}
     [COADVISE grant]
\pers{Amine}{Charfi}{PhD}{AutreEtablissementPublic}
     [COADVISE grant]
\pers{Lamine Mamadou}{Diagne}{PhD}{AutreEtablissementPublic}
     [AUF grant]
\pers{Coralie}{Fritsch}{PhD}{AutreEtablissementPublic}
     [MESR and INRA grant]
\pers{Amel}{Ghouali}{PhD}{UnivEtrangere}
     [AVERROES grant]
\pers{Sonia}{Hassam}{PhD}{UnivEtrangere}
     [COADVISE grant]
\pers{Guilherme}{Pimentel}{PhD}{UnivEtrangere}
     [Univ. Mons (Belgique) and INRA grant]
\pers{Angelo}{Raherinirina}{PhD}{UnivEtrangere}
     [University of Fianarantsoa, Madagascar, LIRIMA grant]
\pers{Radhouene}{Fekih-Salem}{PhD}{UnivEtrangere}
     [AVERROES grant]
     
% --- visiteurs
\pers{Denis}{Dochain}{Visiteur}{UnivEtrangere}    
	[CESAME, Univ. Louvain-la-Neuve (Belgium), 1 month]
\pers{Jaime}{Moreno}{Visiteur}{UnivEtrangere}    
	[UNAM, Mexico City (Mexico), 1 week]
\pers{Hector}{Ramirez}{Visiteur}{UnivEtrangere}    
	[Mathematical Engineering Department, Universidad de Chile, 2 weeks]

% --- stagiaires

\pers{S\'ebastien}{Barbier}{AutreCategorie}{UnivFr}    
	[MSc Student,  Univ. Reims, 6 months]
\pers{Amine}{Boutoub}{AutreCategorie}{UnivEtrangere}    
	[MSc Student,  Univ. Tlemcen (Algeria), 2 months]
\pers{Alejandro}{Rojas-Palma}{AutreCategorie}{UnivEtrangere}    
	[MSc Student,  Univ. Chile, 3 months, INRIA Internship]
	
% --- misc.

\end{composition}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
%%% Section presentation (Overall Objectives)
%%% On peut mettre un ou plusieurs modules.
%%% 
%%% La partie présentation du projet est issue de la section "Overall Objectives" du RAweb 2011 
%%% source : http://raweb.inria.fr/rapportsactivite/RA2011/modemic/uid0.html
%%%
%%% Si les résultats scientifiques de l'année sont importants ou si vous avez reçu 
%%% des prix liés \`a des résultats, alors mentionnez-les dans la rubrique Highlights en fin de la section.
%%% 
%%% Si vous avez un "Best paper" récompensé dans une conférence ou un journal de niveau international, 
%%% citez-le en fin de la section Highlights sous la forme : \bestcite{xxxx}, \bestcite{yyyy}. 
%%% Vous pouvez en avoir plusieurs.
%%% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% http://intranet.inria.fr/disc/publier/raweb2012instructions.html#moduleObjectives

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Présentation du projet issues des informations du RAweb 2011
% Source : http://ralyx.inria.fr/Raweb/modemic/uid3.html
% Date : mardi 4 décembre 2012, 21:52:22 (UTC+0100)
%


%---------------------------------------------------------------------
\begin{module}{presentation}{goal0}{Introduction}

Natural or reconstituted microbial ecosystems are often very complex
(high diversity, interactions within and between species, coupling
with spatial processes: niches, aggregation, biofilm...) \footcite{jessup2004a}.

We bet that  simple models  (in the sense that they are manageable analytically
and/or in a computer) of these ecosystems can explain their main
functions, mainly concerning degradation and conversion.
For this purpose, we investigate population models both deterministic (differential
equations) and stochastic (stochastic differential equations, death-birth processes), as well as individual-based models.



Another challenge is to develop, from expert knowledge and
experimental observations, models that are simple enough (i.e. without
an exhaustive description of all microbial actors) to carry out
model identification and selection as well as the determination of ``control laws'', but realistic enough to be
validated on real processes within a decision-making perspective (i.e. bioprocess control).

One of the main difficulties is to identify the limits of the validity of these models (especially in terms of population size, and of prediction of the coexistence of species). This requires a proper mathematical analysis as well as the development of adapted simulation tools.

\end{module}
%---------------------------------------------------------------------


%---------------------------------------------------------------------
\begin{module}{presentation}{goal1}{Build, simulate and analyze new models of 
microbial ecosystems}

We investigate different models of microbial ecosystems at different scales, that are related to various research questions for better understanding, predicting or piloting real plants.

Eight families of problems are covering our modelling activities:

\begin{enumerate}

\item study the mathematical properties (equilibriums, stability, limit cycles,
bifurcation...) of macroscopic models that distinguish compartments of attached 
and free bacteria.
We are looking for ecological conclusions in terms of coexistence of species.

\item study the mathematical properties of trajectories of a model
that switches from a populational representation by differential equations to an individual-based model
when the population falls below a given threshold. We expect from this
study new insights on validity domains of macroscopic models and 
quantitative estimations of the variability around average trajectories.

\item build a framework for modelling the chemostat with stochastic
processes at a macroscopic scale justified from hypotheses at the individual
level. The classical ``deterministic'' chemostat is expected to be found as an average dynamics for large populations, but second order moments should provide relevant information about the variability about the deterministic approximation.

\item build and simulate IBMs, individual based models \footcite{grimm2005a}, of 1D biofilm and compare
the spatial densities of biofilm and planktonic biomass with
the numerical solutions of 1D PDE models.

The output of this study is to propose and justify 
attachment/detachment terms in the PDE, that are crucial
in the determination of the thickness of the biofilm, and
that are usually chosen in an heuristic way.


\item compare detailed ecological models of a multi-species community at a fine scale 
with low-complexity models at a coarser scale, in the spirit of
the neutral model. 
Within a stochastically varying environment (that is assumed to have
different impacts on each species), the coarse model could describe 
in an effective way the interaction between species and environment as 
a stochastic variability. The goal is to interpret the parameters of the 
global model in terms of properties of the fine-scale model.

\item study chemostat-like models with multi-resources and nutrient recycling,
within the objective of representing microbial activity in soil ecosystems.
The goal is to understand the influence of the choice of hypotheses about the growth terms (dependency in terms of product or minimum functions of each resource) and the recycling terms (from the dead biomass  or during the division process) on
the qualitative behavior of the system and its performances at steady state.


\item investigate the properties of a network of interconnected chemostats
and understand the role of the size of the nodes and the connectivity.


\item couple numerical simulation of fluids dynamics in tanks
with models of biotic/abiotic reactions.
Then, we plan to compare the input/output behavior of these
models with simple representations of networks of 
interconnected chemostats (see the previous point).

\end{enumerate}

\end{module}
%---------------------------------------------------------------------



%---------------------------------------------------------------------
\begin{module}{presentation}{goal2}{Validate hypotheses and identify models with experimental data}

Among our current collaborations and projects (ANR DIMIMOS, ANR DISCO), we have identified five experimental devices 
that we consider relevant for back and forth exchanges
between models and real-world observations for the coming years.
\begin{enumerate}
\item Molecular fingerprints. The LBE (Laboratory of Environmental Biotechnology) at Narbonne is a world leader for one of these techniques,
the SSCP (Single Strand Conformation Polymorphism) that allows to estimate the 
biodiversity of a microbial ecosystem and serves as a comparison 
instrument over time or between ecosystems. A similar kind of signal from the proteins 
expressions is also obtained within the ANR DIMIMOS with the UMR MSE (Microbiologie du Sol et de l'Environnement) in Dijon.
\item Continuous cultures in chemostats. The chemostat device is the typical investigating device in microbiology. Spatial structures can be mimicked and controlled
using interconnected chemostats. Because of contamination risks, 
experimentation in chemostat requires an adequate expertise which the LBE holds.
We plan to launch new such experiments with microbial populations of
interest for specialists of soil ecosystems, in collaboration
with UMR Eco{\&}Sols (Écologie fonctionnelle et biogéochimie des sols et agrosystèmes, Montpellier) and UMR BIOEMCO (Biogéochimie et écologie des milieux continentaux, Grignon).
\item Taylor-Couette reactors (with LBE Narbonne). These bioreactors are specifically designed for the culture of biofilms on {\em coupons}, that can be removed from the system for static analyses of biodiversity (SSCP) and microscopy. Experiments are already scheduled within a task of the ANR DISCO.
\item Flow-cell bioreactors (with Irstea Antony). It consists in small capillary tubular reactors continuously fed by a pump, under a microscope that has been
designed for a continuous acquisition of images. 
We aim to compare biofilm models with 
the information provide by theses images.
\item Micro-plates cultures (with UMR MSE Dijon and LBE Narbonne). 
It contains a hundred of small wells in each of which a microbial community 
is grown in batch on the available substrate. 
Optical density measurements allow one to monitor
simultaneously the biomass growth in the wells. These devices are convenient
to study the effects of different initial compositions of the community
under the same environmental conditions. We believe that it is also
well suited to test neutral-like community models
\end{enumerate}

Each measurement technique requires its own data analysis 
(filters, statistical analysis, image analysis...) to provide information that are
relevant for the models.
On the basis of these experimental observations, qualitative and quantitative validations of the models will be performed. Observers and image correlations are one of the techniques we are using.

\end{module}
%---------------------------------------------------------------------


%---------------------------------------------------------------------
\begin{module}{presentation}{goal3}{Propose new strategies to pilot and optimize microbial ecosystems}

We study optimal design and feedback control laws within the framework of 
ongoing projects, and distinguish two kinds of contributions: 

\begin{enumerate}
\item based on already known models of chemostat or fed-batch reactors, but with explicit spatial considerations, for 

\begin{itemize}
\item the biological treatment of natural water resources, one of the main objective of the associated team DYMECOS with Chile, in collaboration with B. Ivorra from MOMAT (Modelos Matemáticos en Ciencia y Tecnología) group (Madrid) 
and A. Rousseau for the numerical computation of the pollutant spreading,
\item the design of interconnected networks of chemostats, in the following of
the former ARC VITELBIO and also in collaboration with the MOMAT for the comparison and identification with hydrodynamics models.
\end{itemize}

\item based on new models developed in the scope of projects:
\begin{itemize}
\item the Euro-Mediterranean project TREASURE coordinated by the team,
where membranes are at the heart of a new generation of bioreactors
of smaller size and well suited for Southern countries where the temperature 
is not too low. 
\item the ANR DISCO 2010-2013, for which one of the output is expected in terms of control of biofilm reactors.
\end{itemize}

\end{enumerate}

We plan to contribute to the development of new decision making tools to design, control, observe and optimize current and future bioprocesses, for the preservation of natural (aquatic or telluric)
resources, where modelling and numerical simulations are clearly expected, and for the biotechnology industry whose objectives are 
to improve efficiency of bioprocesses under constraints of sustainable development
(energetic consumption, biogas production...)

The tools based on geometric and optimal control of nonlinear systems and possibly 
on viability theory should be enhanced by software developments. 
We also expect to contribute to the numerical determination of
optimal feedback laws for a class of problems relevant for the mentioned applications.
\end{module}
%---------------------------------------------------------------------


%---------------------------------------------------------------------
\begin{module}{presentation}{goal4}{Develop a strategy of software production}

Although the software production is not the main objective of the team,
we aim to assemble models within {\em virtual ecosystems}
(with the objective that it can replace or guide real experiments)
in the four coming years.
Co-developments of simulation software will be looked for within INRIA or outside.
Our working plan is in three steps:
\begin{enumerate}
\item In a first step, we shall develop prototypes or dedicated toolboxes in {\tt Scilab} 
or {\tt Matlab} within the team.
\item Simulations of IBM or PDE require significant efforts, in terms of 
computer implementation and numerical methods. 

The main problem in the implementation of IBM's is the size of the population, 
particularly for applications in microbiology where the size of populations of 
bacteria can be very large. In agent-based models (ABM), population sizes are smaller 
and each individual features sophisticated behavior, while in IBM, population sizes are 
usually larger but with limited individual activities. The population size impacts 
both the execution time and the memory size, but the main bottleneck is the execution 
time because of the communication between the individuals. The idea will be to 
propose, through an object-oriented approach, data structures that will limit this 
communication. From the hardware point of view, grid computing could improve execution 
time but only on a limited range.  
These activities will have to be developed in association with 
specialists for our most ambitious developments: MOMAT already cited but also 
researchers from I3M (Institute of Mathematics and Mathematical Modelling of Montpellier) University of Montpellier 2/CNRS.

\item For the design and development of user-friendly and graphical interfaces
that need to be easily accessible by biologists and bioprocess engineers,
we shall look for the help of service companies 
specialized in agronomy and biotechnology applications (such as ITK Company, \url{http://itkweb.com}).
\end{enumerate}


\end{module}
%---------------------------------------------------------------------



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
%%% module Highlights (Faits Marquants)
%%% 
%%% C'est ici que vous mettrez les \bestcite si vous en avez.
%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% Les Highlights (Faits Marquants) doivent être relatifs aux résultats de votre équipe. 
%%% Seuls les résultats scientifiques importants ou des prix liés \`a des résultats justifient la présence de la rubrique Highlights.

%---------------------------------------------------------------------
\begin{module}{presentation}{Highlights}{Highlights}

{\it
\begin{itemize}

\item
The characterization of interconnections of chemostats that provide
a global stability of bioprocesses with inhibition, mentioned in Section
\ref{theory_chemostat}, has led to a patent application by INRA \cite{patent2012}.


\item
We have proposed a model of fouling dynamics of membrane \cite{charfi2012}. Our aim in the future is to introduce the fouling dynamics in the AM2 model \cite{benyahia2012c}.


\item
We have proposed hybrid models (deterministic/stochastic and continuous/discrete) of population dynamics as alternatives to conventional models based on ordinary differential equations. The later models are  generally accepted as a good approximation of the former ones in large population asymptotic, but even in very large population size the two groups of models present drastically different behavior, notably in terms of persistence properties  \cite{campillo:hal-00723793}, see Section \ref{sec.recent.stochmodel}.


\end{itemize}
}

\end{module}
%---------------------------------------------------------------------


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
%%% Section  fondements (Scientific Foundations)
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\begin{module}{fondements}{axis1}{Modelling and simulating microbial ecosystems}

Microbial ecosystems naturally put into play phenomena at different scales, from the individual level at a microscopic scale to the population level at a macroscopic scale, with sometimes intermediate levels.
The size of substrate molecules is a thousand time smaller than the size of microorganisms and usually diffuse much faster.
The substrate consumption of one microorganism is negligible at the population level but the sum of the consumption of its neighbors can modify the local concentration of substrate, which itself modifies microorganism growth, acting as a {\em feedback loop}.
For other variables that change slowly (pH, temperature...) cumulative effects create
intermediate time scales, coupling individual and environment dynamics.
The very large populations justify macroscopic modelling but for some ecosystems, spatial structures seen at intermediate scale need to be tackled. This is typically the case of biofilm ecosystems, for which the biofilm structure is responsible of characteristics of the overall ecosystem.
Models that are purely individual-based or purely populational
are rarely truly satisfactory to incorporate current knowledge on microbial ecosystems at various scales
and to push ahead mathematical analysis or to derive operational rules.

%......................................................................
\subsubsection{Macroscopic models}

The starting point is the knowledge of biologists that report a large number of mechanisms
discovered or shown on laboratory experiments at a population level, such as
competition for a growth-limiting substrate,
predation interactions,
obligate mutualism
or
communication between bacteria.
If each {\em elementary} mechanism is today well understood and modelled at a macroscopic level,
the consideration of several mechanisms together in a single model is still raising several questions of
understanding and prediction. This is typically the case when there is more than one growth-limiting substrate in the chemostat model or when one couples species competition with a spatial structure (flocculation, niches...).

\begin{enumerate}
\item {\em Non-spatial models.}\\
Ordinary differential equations (ODE) are the common way to describe the evolution of the size or concentration of species populations and their functional contribution in resource transformation (such as substrate degradation) in homogeneous or perfectly mixed compartments (or ecological niches).
The well-known chemostat model \footcite{SmithWaltman95a} used in microbiology for single strain:
\[
\begin{array}{lll}
 \dot s & = & -\frac{1}{y}\mu(s)\,b+D\,(s_{in}-s)\\
 \dot b & = & \mu(s)\,b -D\,b
\end{array}
\]
(where $s$ and $b$ stand respectively for the substrate and biomass concentrations, $\mu(s)$ is specific growth function, $D$ the dilution rate, $s_{in}$ the input substrate concentration), has to be extended to cope with the specificity of microbial ecosystems in the following directions.
\begin{itemize}
\item very large number (hundreds or thousands) of species. This leads to the problem of characterization of their distribution during the transients, that is a way to study the {\em functional redundancy} of ecosystems.
\item environmental fluctuations (input flow rate, input concentration, temperature, pH...). This impacts the efficiency of a microbial ecosystem, when biological and environmental time scales are different.
{\em Singular perturbations} is the technique we use to separate {\em slow}
variables from {\em fast} ones, leading to approximations of the dynamics on {\em slow manifolds}
to be determined and analyzed.
\item interactions due to several limited resources and trophic chains. Most of the literature on the chemostat considers models with single limited resource, while some work studied purely essential or substitutable resources.
\item several populations of bacteria (for each species) to describe the effects of certain spatial structures that are artificially created in bioreactors or naturally found in soils, like flocks, colonies or biofilms: the planktonic (or free) cells and the biofilm (or fixed) biomass (for telluric ecosystems, such a distinction
is also relevant to represent the sticking/non sticking characteristics of soil).
Considering simple models of aggregates (that are not spatialized) can provide a simplified model of the dynamics of the overall biomass. \item {\em active} and {\em dormant} bacteria. This distinction is motivated by the observations made on ecosystems of sparse resources such as arid soils.
\end{itemize}

\item {\em Spatial models.}\\
In the spirit of lattice differential equations,
representations in terms of networks of (abstract) interconnected bioreactors
propose an intermediate level between models
of average biomass (a single ODE) and a continuous representation of space (PDE).
A model of interconnected bioreactors is a way to {\em implicitly}
take into account spatial heterogeneity, without requiring a precise
knowledge of it. It is similar to the island models used in ecology
\footcite{MacArthurWilson67a} but coupled with the dynamics of abiotic resources and hydrodynamics laws (transport, percolation, diffusion) governing the transfers between patches. This approach appears to be relevant for telluric ecosystems, for which pedologists report that microbial activities in soil are usually concentrated in {\em hot-spots} that could be seen as small bioreactors.
Understanding the role of the topology of the interconnection network
and how a spatial structure impacts the outputs is also relevant in biotechnology to improve the yield or stability of processes.
\end{enumerate}


%......................................................................
\subsubsection{Microscopic models}

In 
these models (birth and death processes, neutral models, individual-based models) 
the dynamic of the population is described in terms of discrete events: birth and 
death of individuals, or jumps in terms of biomass. These models can be gathered 
under the same framework that could be called \emph{Markov stochastic processes 
with discrete events}. Most of the time they should be coupled with continuous 
components like the size of each individual or the dynamic of the resources 
(represented in terms of ODE or PDE).

The Markovian framework allows on the one 
hand sharp analyses and rescaling techniques \footcite{ethier1986a}; on the other hand it 
induces a simplification in the memory structure of the process that is important in terms of 
simulation. Indeed, as the future state of the system depends from the past only 
through the present state, only the current state should be kept in memory for 
simulation.

We will consider three families of processes with discrete events, from simplest 
to most complex.
\begin{enumerate}
\item {\em Birth and death processes.}\\
 These models \footcite{feller1968a} are of first importance in small 
population size. They indeed allow investigation of near-to-extinction situations in 
a more realistic ways than the classical ODE models: they permit the computation, 
analytically but most of the time numerically, the distribution of extinction time 
and the probability of extinction.  Efforts should be made to developed efficient 
Monte Carlo simulation procedures and approximation techniques for extinction 
probability and time distribution evaluation. In larger population sizes, they are 
advantageously approximated by diffusion models (see next section).

\item {\em The neutral models.}\\
 In {\em neutral} models \footcite{hubbell2001a} sizes of different species
evolve as birth and death processes with immigration: all individuals have the same
characteristics and are not spatialized. Such hypotheses could be considered
unrealistic from a purely biological perspective, but these models focus on some
precise properties to be simulated and predicted (for instance the biodiversity).

Comparing the prediction of species abundance of
these models to real observations provides a way to justify or invalidate the
neutral hypothesis.
Extensions of the neutral model, that was
originally introduced for forest ecology, have to be developed in order to better suit the framework of
microbial ecology, such as the non constant size of the populations and spatialized variations.



\item {\em The individual based models.}\\
 IBM's \footcite{deangelis1992a,dieckmann2000a} appear to be well suited to describe 
colonies or biofilms \footcite{wanner2006a}: in addition to birth, death and movement events, one has to 
consider {\em aggregation} and {\em detachment} events. The mechanisms that lead to 
the emergence of spatial patterns of colonies, or the formation of biofilms, which 
adhere to surface via polymers generated by the bacteria under specific hydrodynamics 
conditions, are not well understood yet. Typically, one can consider that bacteria 
inside the aggregates are disadvantaged to access the nutrient.

\end{enumerate}

IBM modelling is a convenient way to propose aggregation and detachment mechanisms at 
the individual level in terms of random events connected to the geometry of the 
neighborhood, and to compare generated images with microscopic observations 
(for instance the confocal microscopy).

One has to be aware that few methods are available to study systematically and rigorously the properties of IBM, contrary to models based on differential equations (ODE, PDE...).

%......................................................................
\subsubsection{Bridges between models}

The ``theory of a computational model'', that combine two kinds of models (typically ODE and IBM)
that are different representations of the same objects,
relies on two steps: the ``program making'' and the ``theoretical study'', in the spirit of the {\em double modelling} approach (roughly speaking, it consists in grasping the complexity of a IBM by analyzing accurately the consequences of each hypothesis on the macroscopic behavior of the model, building an approximate model of its global dynamics).
Two main tools can be considered.

\begin{enumerate}
\item {\em Change of scale.}\\
For IBM models (neutral or Markovian), we consider mean field and moments approximation techniques 
that provide 
information at the macroscopic (i.e. populational) level, to be compared with macroscopic models.
From a birth-and-death process  describing the individual level, a renormalisation can provide a stochastic differential equation at a meso-scale.
The {\em diffusion approximation} technique can be understood as a numerical acceleration technique where the number of births and deaths follows a normal law.
These stochastic models at meso-scale can provide additional information compared to deterministic models at a macro-scale, such as parameter identifiability or finite time extinction.
The price to pay is to give much more conceptual and numerical efforts,
 that become less relevant for very large populations.
 
For PDE models on spatial domains described with regular patterns (such as models of biofilm), the homogenization technique allows to obtain simpler PDE with constant parameters.

\item {\em The multi-scale modelling.}\\
The spatial heterogeneity in microbial ecosystems requires to consider 
simultaneously several scales:
\begin{itemize}
\item a {\em physical} scale. In batch processes, nutrient diffusion can be modelled by adapting the heat equation with Dirichlet boundary conditions. In continuous reactors, a convection-diffusion equation with Neumann boundary conditions is considered instead, the speed vector field being provided by the equations of fluid mechanics.
The spatial scale used for the discretization is given by diffusion and flow 
parameters.
\item a {\em biological} scale, given by the size and mobility of bacteria. Usually, 
this scale is larger than the physical one (at least in the liquid phase).
\item an {\em aggregation} scale of colonies or biofilms, even larger, that provides the
spatial patterns.
\end{itemize}
It is always possible to describe all the processes at the smaller common scale
and then use a global representation, but this leads to extremely long
computation times. The challenge is to manage these overlapping scales
together and guarantee the stability of the numerical schemes. This is
the goal of the {\em multi-scale} approaches \footcite{Lesne2006a}. For microbial ecosystems, it consists in
\begin{enumerate}
\item proposing new representations of the various scales of aggregation of bacteria in a model, taking into account the attachment-detachment processes determined by the local hydrodynamics conditions. Here, discussions with specialists of fluid mechanics are required.

\item coupling diversity models (e.g. models based on the neutral assumption) with spatial models
(that reproduce the patterns observed on images of microscopy) to better understand the link biodiversity/structure.

\item introducing new  {\em control} variables, considered as independent variables, each of them describing a proper scale. For this purpose, we investigate different techniques available to determine such variables:
{\em mean-field} approximation,
{\em singular perturbations}, 
{\em unification by limiting layers} 
or
\item {\em renormalising}, that  aims at detecting invariants among models of different scales.

\end{enumerate}
\end{enumerate}
\end{module}
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\begin{module}{fondements}{axis2}{Interpreting and analyzing experimental observations}

The validation of microbial models on data is rarely a straightforward task, because observations are most of the time not directly related to the variables of the models.
Techniques such as abundance spectrum provided by molecular biology or confocal imagery are relatively recent in the field of microbial ecosystems. The signals provided
by theses devices leave many research questions open in terms of
data interpretation and experiments design.
One can distinguish three kinds of key information that are needed at the basis of model assumptions:
\begin{itemize}
\item structure of the communities (i.e. who is present?),
\item nature of interactions between species (competition, mutualism, syntrophism...),
\item spatial structure of the ecosystems.
\end{itemize}

%......................................................................
\subsubsection{Assessment of community structures}


Ecosystems biodiversity can be observed at different levels, depending on the kind of observations. One usually distinguish:
\begin{enumerate}
\item {\em The taxonomic diversity.}
Several techniques developed by molecular biologists
can gather information on the genetic structure of communities:
\begin{itemize}
\item {\em sequencing of a given gene in the community.} The RNA 16S gene is often chosen
to identify bacteria or Archeae.
\item {\em molecular fingerprints.} Some regions in the sequence of the RNA 16S gene
encode faithfully the taxa species and can be amplified by PCR techniques.
\item  {\em the sequencing of the overall genetic material of a community} (meta-genomic)\end{itemize}
All these techniques bring new problems of data interpretation to estimate in a robust manner the properties of communities. The signals are combinations of contributions of abundances from each taxon. For an ecosystem with a limited diversity, composed of known species, the signal allows to determine with no ambiguity the abundances. In natural ecosystems, the signal is more complex and it is hopeless to determine uniquely the taxa distribution.

\item {\em The functional diversity.} It is usually observed at a larger scale, measuring the performances of the overall ecosystem to convert organic matter.
The taxonomic diversity does not usually provide such information (it is possible to study {\em functional genes} but this is much more difficult than studying the 16S one).

A convenient way to study the functional performance of microbial
community dynamics is to grow the same microbial community on
different substrate compositions, and monitor its performance on these different substrates.
Neutral community models \footcite{hubbell2001a} provide a reference for what would
happen if no functional differences are present in the community. The
deviation of experimental observations from neutral model predictions
can be considered as a measure of functional diversity.

\end{enumerate}

Understanding the links between taxonomic and functional diversity
is currently a tremendous research question in biology
about genotype/phenotype links, that one can also find in the specific context of microbial ecosystems.

%......................................................................
\subsubsection{Characterization of the interactions}

The role of biodiversity and its preservation in ecosystems are research questions
currently largely open in ecology. The nature and number of interactions
between bacterial populations are poorly known, and are most probably a key to understand biodiversity. In the classical chemostat model, inter-specific interactions are rarely considered. Also in theoretical ecology, interaction information is typically encoded in an {\em interaction matrix}, but the coupling with common abiotic resources and the stoichiometry is hardly addressed in the models. 

The information provided by confocal microscopy is also a way to estimate the distance of interactions between microorganisms and substrates. This knowledge is not often documented although it is crucial for the construction of IBM.




%......................................................................
\subsubsection{Observation of spatial structures}

Schematically, one can distinguish two origins of spatialization:

\begin{enumerate}
\item due the physics of the environment. In bioprocesses, this happens typically for
large tank size (inducing {\em dead zones}) or sludge accumulation making the suspension closer from a porous medium than a liquid one.
Numerical experimentation can be driven, coupling a
solver of the equations of the fluid mechanics with microbiology equations. Then, the spatial distribution of the biomass can be observed and used to calibrate simpler models.
Typically, a dead zone is modelled as a
diffusive interconnection between two perfect (abstract) tanks.

But the biotechnology industry aims at considering more sophisticated devices than simple tanks. For instance, the fluidized bed technique consists in creating a counter-current with oxygen bubbles for preventing the biomass to leave the rector.
In more complex systems, such as soil ecosystems,
it is difficult to obtain faithful simulations because
the spatial structure is rarely known with accuracy. Nevertheless,
local observations at the level of pores can be achieved,
providing information for the construction of models.
\item due to the formation of aggregates (flocks, biofilms...) or biomass wall attachment.
Patterns (from ten to a hundred micro-meters) can be observed with
confocal microscopy.

Spatial distribution of bacteria, shape of patterns and composition of the aggregates help to express hypotheses
on individual behaviors.
But quantification and variability of images provided by confocal
microscopy are difficult. An open question is to determine the relevant morphological indicators that characterize aggregation and
the formation of biofilms.
\end{enumerate}

\end{module}
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\begin{module}{fondements}{axis3}{Identifying, controlling and optimizing bioprocesses}

The dynamics of the microbial models possess specificities that do not
allow the application of the popular methods of the theory of
automatic control
\footcite{BastinDochain90a}, such as linear control, feedback linearization or canonical forms.
\begin{itemize}
\item positivity constraints. State variables, as well as control inputs, have to stay non-negative (input flow pump cannot be reversed because of contamination issues).
\item non-linearity. Several models have non-controllable or non-observable linearizations when inhibition effects are present (i.e. change of monotonicity in the growth curves).
\item model and measurement uncertainties. In biology, it is rarely relevant to consider model uncertainties as additive Gaussian or finite energy signals.
\end{itemize}

%......................................................................
\subsubsection{Software sensors and identification}

Sensors in biology are often poor and do not provide the measurements
of all the state variables of the models: substrate, strain and product
concentrations.
In addition, measurements are often spoilt by errors. For instance
optical density measurements give an indirect measure of the biomass, influenced by abiotic factors that share the same medium.

Analytical techniques are well suited to ODE models of small dimension, such as:
\begin{itemize}
\item guaranteed set-membership observers, when the system is non observable or in presence of unknown inputs,
\item (non-linear) changes of coordinates, when the system is observable but not in a canonical form for the construction of observers with exponential convergence. 
\end{itemize}

Software sensors can be also derived with the help of simulation based approaches like particle filtering techniques \footcite{doucet2001a,del-moral2004a}. This method is suited to diffusion models that approximate birth and death processes. Such softwares will allow us to investigate the different sources of randomness: demography, environment, but mainly imprecision of the sensors.

Similarly, identification techniques for constant parameters are based on sensor models as well as demography and environmental randomness models. In this case, Bayesian and non-Bayesian statistical techniques can be used \footcite{campillo2009a,gilks1996a}.

%......................................................................
\subsubsection{Bioprocess stabilization}

In bioprocesses, the most efficient bacterial species at steady state
are often inhibited by too large concentrations of substrates (this corresponds
to assuming that the growth function  $s \mapsto \mu(s)$ in the
classical chemostat model is non-monotonic).
This implies that the washout equilibrium
(i.e. disappearance of the biomass) can be attractive, making the bioprocess bi-stable.

A common way to globally stabilize the dynamics toward
the efficient equilibrium is to manipulate the dilution rate $D$ \footcite{BastinDochain90a}. But a diminution of the input flow rate for the stabilization
requires to have enough room for an upstream storage, which is an expensive solution
especially for developing countries that need to be equipped with new installations.

Alternative ways are proposed to stabilize bioprocesses
without restricting the input flow rate:
\begin{itemize}
\item either by {\em physical means}, in terms of recirculation and bypass loops, or membranes as a selective way to keep bacteria and their aggregates inside the tank
and improve its efficiency.
\item either by {\em biological means}. The {\em biological control}
consists in adding a small quantity another species with particular growth characteristics, that will help the other species to win the competition in the end.
\end{itemize}


%......................................................................
\subsubsection{Optimal control of bioreactors}

The filling stage of bioreactors, or ``fed-batch'', is often time consuming
because the quantity of initial biomass is small and consequently the population
growth is slow. The minimal time is a typical criterion for designing a filling strategy, but the optimal feedback synthesis is non trivial and may present singular arcs
when the growth function is non-monotonic \footcite{Moreno1999}.

Recent progress have been made in the consideration of
\begin{itemize}
\item multi-species in sequential reactors (having more than one strain makes significantly more difficult to analyze singular arcs because of the higher dimensions of the state space, and there is little literature on the subject),
\item energy consumption of flow pumps and the value of byproducts of the biological reactions such as biogas in the criterion (instead of minimal time or as penalties).
Recent concerns about sustainable development encourage engineers to look for compromises between those objectives under constraints on output concentrations.
\end{itemize}

%......................................................................
\subsubsection{Plant design and optimization}

We distinguish two kind of setups:

\begin{enumerate}
\item {\em The industrial setup.}
A research question, largely open today, is to identify networks of  interconnections of bioreactors that are the most relevant for industrial applications in terms of the following objectives:
\begin{itemize}
\item reasonably simple configurations (i.e. with a limited number of tanks and connections),
\item significant improvement of the residence time at steady state over single or simpler configurations, or shapes of the reservoirs such that the total volume required for a given desired conversion factor at steady state is reduced.
\end{itemize}

\item {\em The bioremediation setup.}
Typically, the concentration of pollutant in a natural reservoir is solution of a transport-diffusion PDE,
but the optimal control of the transport term is  almost not studied in the literature.

%An approach consists in finding satisfactory approximations of the solutions of transport-diffusion-reaction PDE (for which the Eulerian speed of the fluid is determined by the Navier \& Stokes equation), in terms of a network of ODEs, that makes effective the application of the Pontryagin Maximum Principe.
\end{enumerate}

\end{module}
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\begin{module}{domaine}{water}{Preservation of water resources}

The biological decontamination of wastewater is our main application domain,
in the continuation of the long collaboration
with the INRA research laboratory LBE.
We target applications from the decontamination industry, held by large groups
as well as small companies specialized in specific pollutants (for instance in
fish farming). We aim also to study connected application domains for
\begin{itemize} 
\item the aquatic ecology where microorganisms 
play an important role in the quality of natural water resources,
\item the re-use of water in arid climates for countries of North of Africa, within the euro-Mediterranean project TREASURE.
\end{itemize}

\end{module}
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\begin{module}{domaine}{soil}{Microbial ecology of soil}

This application domain is more recent for the team members. We target
\begin{itemize}
\item the research questions raised by agronomists, about the better understanding of the interactions and the biodiversity of microbial communities in soils,
with the help of models and numerical simulations,
\item the role of spatial structures on the functions or
{\em ecological services} of microbial ecosystems, notably the soil fertility
and the carbon sequestration.
\end{itemize}
\end{module}
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\begin{module}{domaine}{fermentation}{Control of fermentation processes}


Very closely to our studies about wastewater bioreactors and chemostat models,
we target applications in fermentation processes:
\begin{itemize}
\item either for agro-food products. A typical application is the control
of  cascade fermenters in the study of wine fermentation with UMR SPO
(Sciences Pour l'\OE nologie, Montpellier), within the European project CAFE.
\item either for the green chemistry.
A typical application is the consideration of spatialization in enzymatic models
of production of agro-polymers with UMR IATE (Ingénierie des Agro-polymères et Technologies Émergentes, Montpellier).
\end{itemize}
\end{module}
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\begin{module}{domaine}{digestion}{Animal digestive ecosystem}


Ruminants absorb plant cells, mainly constituted by cellulose, from which
the microbial population of their digestive system
extracts carbon and energy to provide proteins and energetic molecules.
This bio-conversion produces also important quantities of methane, a gas responsible of part of the greenhouse effect (the billion of cows on earth
reject 20\% of the methane linked to human activities). INRA researchers
have shown that this methane production could be reduced by
30\%\ by changing the proportion of fat acids in the their food, that
also implies that the composition of their microbial ecosystem is modified.

This application domain of the microbial ecology is at an early stage.
URH team (Unité de Recherche sur les Herbivores, Clermont) has developed an artificial rumen that is close to a chemostat, for testing different kind of nutrition diets.
Preliminaries contacts have been taken, and a modelling demand has been clearly formulated and will be taken up my MODEMIC. This theme falls into the research priorities for
the environment preservation.

\end{module}
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%%% Information sur les donn\'ees import\'ees : logiciels
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%%% Les logiciels pr\'esent\'es ici sont export\'es depuis la base Inria des logiciels (BIL)
%%% La BIL \'etant en cours de d\'eveloppement, il n'y a pas encore d'interface
%%% de d\'ep\^ot ou de modification de logiciels.
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%%% Url de consulation : http://bil.inria.fr/
%%% En cas de probl\`eme BIL : raweb-support@inria.fr
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\begin{module}{logiciels}{VITELBIO}{VITELBIO}
\label{module.logiciels.VITELBIO}

\begin{participants}
\pers{J\'er\^ome}{Harmand}, \pers{Alain}{Rapaport}
\end{participants}
VITELBIO (VIrtual TELluric BIOreactors) is a simulation tool for studying networks of interconnected chemostats with the objective of mimicking microbial activities in soil.
The software, developed with the
help of ITK Company, is accessible on a server from any web navigator
and make use of Flex for the user interface and Octave for the numerical integration.
An important effort has been made for obtaining a pleasant
and easy interface that is appealing for microbiologists: the network
can be drawn graphically on the screen and simulation results
can be easily compared between (virtual) experiments, superposing
trajectories curves.

This software is used by several researchers,  from LBE (INRA Narbonne), UMR Eco \& Sols (Montpellier), UREP (Unité de Recherche sur
l'Ecosystème Prairial, INRA Theix), Biomeco (Paris-Grignon), UMR EGC (Environnement et grandes cultures, Paris-Grignon)... and also as a teaching support.
Viltebio is presented at \url{http://sites.google.com/site/vitelbio/} and it is accessible at \url{http://vitelbio.itkweb.fr}.

\end{module}
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\begin{module}{logiciels}{SMC DEMOS}{SMC DEMOS}
\label{module.logiciels.SMCDEMOS}

\begin{participants}
\pers{Fabien}{Campillo}
\end{participants}

SMC DEMOS (Sequential Monte Carlo demos) proposes a set of
demonstration Matlab procedures for nonlinear  filtering approximation
via particle filtering (sequential Monte Carlo): bearing-only tracking
with obstacles, tracking in digital terrain model, track-before-detect in
a sequence of digital picture, mobile phone tracking based on the
signal strength to nearby antenna. This software is deposited with the
``Agence pour la Protection des Programmes'' (APP, 7/7/2009),
available at 
\htmladdnormallink{http://www-sop.inria.fr/members/Fabien.Campillo/software/smc-demos/}{http://www-sop.inria.fr/members/Fabien.Campillo/software/smc-demos/}.

\end{module}
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%%% Section Resultat nouveaux
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\begin{module}{resultats}{theory}{Theoretical results}

%......................................................................

\subsubsection{Models resource/consumer}
\label{theory_chemostat}
The team maintains a significant activity about the theory of the
chemostat model, proposing and studying extensions of the classical models. 

\paragraph{Theory of competition and coexistence}

\begin{participants}
 	\pers{Jérôme}{Harmand}
	\pers{Claude}{Lobry}
 	\pers{Tewfik}{Sari}
\end{participants}

In the papers \cite{Sari2,lobry:hal-00711218}  we consider deterministic models of competition. We study the persistence of species. In \cite{sari2012} we study a syntrophic relation between microbial species. In \cite{Sari5}, we give a global asymptotic stability result for a mathematical model of
competition between several species in a chemostat, by using a new Lyapunov function. The model includes
both monotone and non-monotone response functions, distinct removal rates for the species and variable
yields, depending on the concentration of substrate.




%......................................................................
\paragraph{Study of interconnected chemostats}

\begin{participants}
        \pers{Jérôme}{Harmand},
	\pers{Alain}{Rapaport}
\end{participants}

We have shown how a particular spatial structure with a buffer
globally stabilizes the chemostat dynamics with non-monotonic response
function, while this is not possible with single, serial or parallel
chemostats of the same total volume and input flow.
We give a characterization of the set of such configurations
that enjoy this property, as well as the configuration that
ensures the best nutrient conversion.
Furthermore, we characterize the minimal buffer volume
to add to a single chemostat for obtaining the global
stability. These results are illustrated with the Haldane function
that models inhibition in micro-organisms growth \cite{rapaport2012}.

In industrial applications, the attraction of the wash-out
equilibrium is undesired because it presents a risk that may
ruin the culture in case of disturbance, temporarily pump breakdown
or presence of toxic material that could drive the state in the
attracting basin of the wash-out equilibrium. This approach has led to
a patent deposit by INRA \cite{patent2012} during the PhD of H. Haidar,
a former PhD student of the team \footcite{HaidarThesis}.

%......................................................................
\paragraph{Aggregation models in the chemostat}

\begin{participants}
        \pers{Radhouene}{Fekih-Salem},
        \pers{J\'er\^ome}{Harmand},
	\pers{Claude}{Lobry},
	\pers{Alain}{Rapaport},
 	\pers{Tewfik}{Sari}
\end{participants}

We have studied a model of the chemostat where the species are
present in two forms, isolated and aggregated individuals, such as
attached bacteria in biofilm or bacteria in flocks. We show that our general
model contains a lot of models that were previously considered in the
literature. Assuming that flocculation and deflocculation dynamics are
fast compared to the growth of the species, we construct a reduced chemostat-like model in which both the growth functions and the apparent dilution rate depend on the density of the species. We also show that such a model involving monotonic growth rates may exhibit bi-stability, while it
may occur in the classical chemostat model, but when the growth rate
is non monotonic \cite{fekih2013,Sari14}. This work is part of the PhD of
R. Fekih-Salem co-supervised by A. Rapaport and T. Sari.

This research subject has been mainly motivated by the DISCO project
(see Section \ref{module.contrats.DISCO}).

%......................................................................
\paragraph{Overyielding in continuous bioprocesses}
\begin{participants}
    \pers{Denis}{Dochain},
	\pers{Alain}{Rapaport}
\end{participants}

We have shown that for certain configurations of two chemostats fed in
parallel, the presence of two different species in each tank can
improve the yield of the whole process, compared to the same
configuration having the same species in each volume. This leads to a
(so-called) ``transgressive over-yielding'' due to
spatialization \cite{dochain:hal-00726364}.

This work has been achieved during the stay of Prof. P. de Leenheer (Univ. Florida).

%......................................................................
\subsubsection{Measuring taxonomic diversity of microbial communities}
\label{SectionMicrobDiv}

\begin{participants}
	\pers{Bart}{Haegeman}
\end{participants}

Diversity is considered to be a main determinant of the behavior of microbial communities. However, measuring microbial diversity is challenging. Although metagenomic techniques allow us to sample microbial communities at unprecedented depths, the disparity between community (e.g., $10^{15}$ organisms) and sample (e.g., $10^5$ organisms) remains large. We have studied what the diversity observed in a sample tells us about the real diversity of the community.

For a given empirical sample the aim is to construct the community from which this sample was taken. It turns out that a large set of community structures are consistent with the sample data. Some diversity metrics vary widely over this set of consistent communities, and are therefore difficult to infer from the sample data. Other diversity metrics are approximately constant over the set of consistent communities, and are therefore much easier to infer from the sample data.

The analysis of the set of consistent communities has yielded the following insights. First, it is impossible to robustly estimate  the number of species from sample data. This is easy to understand.  Microbial communities typically contain a large number of rare species, and these rare species are unlikely to be present in the sample. Hence, sample data are lacking crucial information to estimate species richness. Second, other diversity metrics, in particular Shannon and Simpson diversity, can be robustly estimated  from sample data. We have constructed lower and upper estimates for a general class of diversity metrics, and we have shown that the difference between the extremal estimators, that is, the estimation uncertainty, is small for Shannon and Simpson diversity.


%......................................................................
\subsubsection{A theory of genetic diversity within bacterial species}
\label{SectionGeneDiv}

\begin{participants}
	\pers{Bart}{Haegeman}
\end{participants}

With the wide availability of DNA sequencing, microbiologists are now able to rapidly sequence entire bacterial genomes. Comparison of these genomes has revealed a large genetic diversity within bacterial species. For example, one genome of the bacteria \emph{E.~coli} has about 4000 different genes, but a set of 10 genomes of \emph{E.~coli} has typically over 10000 different genes. Some of these genes are shared by all or almost all of the genomes, but many other genes are only present in one or a few of the genomes. This observation has important implications for the definition of bacterial species and for the description of the functional characteristics of bacteria.

In \cite{haegeman2012} we propose a theory for the frequency distribution of genes within a set of genomes. The model describes the genetic diversity as a balance between two forces. Demographic processes such as division and death tend to reduce the genetic diversity; horizontal gene transfer from other species can increase the genetic diversity. Our model predicts that the gene frequency distribution is U-shaped, meaning that there are a large number of genes present in only a few genomes, a small number of genes present in about half of the genomes, and a large number of genes present in almost all genomes. This prediction is consistent with the gene frequency distributions of six bacterial species we have analyzed (about 100 sequenced genomes in total). Importantly, the model does not assume any functional difference between the genes, that is, genes are considered to be selectively neutral. By showing that empirical gene frequency distributions can be reproduced by a neutral genome model, we contend that the frequency of a gene should not be interpreted as an indication of its essentiality or importance.


%......................................................................
\subsubsection{Individual-based modelling for bacterial ecosystems}
\label{sec.recent.ibm}

\begin{participants}
	\pers{Fabien}{Campillo},
	\pers{Chlo\' e}{Deygout},
	\pers{Coralie}{Fritsch},
	\pers{Jérôme}{Harmand},
	\pers{Marc}{Joannides},
	\pers{Claude}{Lobry}
\end{participants}


In terms of computational modelling of ecosystems, individual-based models (IBMs) are an interesting path to explore. We can outline two types of IBMs. On the one hand ``detailed IBM'' attempt to integrate in an ad-hoc way all the knowledge available about an ecosystem. On the other hand, ``simplified IBM'' are limited to one or several mechanisms to simplify the analysis. The former may be more realistic but are often difficult to analyze. Although the latter are too simplistic in realistic situations they lend themselves to the analysis and numerical analysis. We focus on the latter.

The IBMs offer an interdisciplinary language between biologists, biotechnologists, mathematicians, and computer scientists, to develop models in the form of relatively simple rules. In the case of simplified IBMs it is possible to translate these rules in the form of a branching Markov process with values in a space of measures. Using scaling methods, the IBMs can be approximated by integro-differential equations; using model simplification methods IBMs can be reduced to stochastic or ordinary differential equations. The mathematical interpretation of the IBMs and their analysis is relatively recent and still very few studies exist \footcite{fournier2004a}. The numerical analysis of these models is yet to be built. Under certain conditions, IBMs themselves can be simulated through adapted Monte Carlo procedures.

The MODEMIC project-team develops many studies in the field of IBMs. The first is part of the ANR MODECOL on the modelling of clonal plant growth
(see Section \ref{module.contrats.modecol});
the second is part of the ANR DISCO on modelling of biofilms
(see Section \ref{module.contrats.DISCO});
the third is also part of the ANR DISCO is dedicated to the modelling of biofilms in plug-flow reactors  (see Section \ref{sec.ibm.disco}); the last one is the ongoing thesis of Coralie Fritsch at the \'Ecole Doctorale I2E of the University of Montpellier 2, under the supervision of Fabien Campillo and J\'er\^ome Harmand. The thesis aims at developing and analyzing ``simple'' individual-based microbial ecosystems models.




In all cases, we aim at developing the Monte Carlo simulation of the IBM as well as analyzing their links with integro-differential models. We also seek to make connections with non-IBM models proposed in Section \ref{sec.recent.stochmodel}.



%......................................................................
\subsubsection{Stochastic/discrete and stochastic/continuous modelling for biotechnology and population dynamics}
\label{sec.recent.stochmodel}

\begin{participants}
	\pers{Fabien}{Campillo},
	\pers{Marc}{Joannides},
	\pers{Claude}{Lobry}
\end{participants}

In \cite{campillo2012c}, we consider a stochastic model of the two-dimensional chemostat as a diffusion process for the concentration of substrate and the concentration of biomass. The model allows for the washout phenomenon: the disappearance of the biomass inside the chemostat. We establish the Fokker-Planck equation associated with this diffusion process, in particular we describe the boundary conditions that modelize the washout. We propose an adapted finite difference scheme for the approximation of the solution of the Fokker-Planck equation. 


In \cite{campillo:hal-00723793}, we consider a hybrid version of the classical predator-prey differential equation model. The proposed model is hybrid: continuous/discrete and deterministic/stochastic. It contains a parameter $\omega$ which represents the number of individuals for one unit of prey -- if $x$ denotes the quantity of prey in the differential equation model $x = 1$ means that there are $\omega$ individuals in the discrete model  -- is derived from the classical birth and death process. It is shown by the mean of simulations and explained by a mathematical analysis based on results in singular perturbation theory (the so called theory of Canards) that qualitative properties of the model like persistence or extinction are dramatically sensitive to $\omega$. This means that we must be very cautious when we use continuous variables in place of jump processes in dynamic population.



%......................................................................
\subsubsection{Optimal control of continuous bioprocesses}
\label{optimal-control}
\begin{participants}
	\pers{Walid}{Bouhafs},
	\pers{Amel}{Ghouali},
	\pers{J\'er\^ome}{Harmand},
	\pers{Alain}{Rapaport}
\end{participants}

In continuous bioprocesses, a usual objective is to stabilize the output of the bioreactors about a desired steady state (in wastewater industry, this value is typically chosen under the norm of authorized discharge). It happens more and more frequently that transient trajectories are expected also to maximize a product of interest.

We have begun to study the maximization of the gaseous production of methane in anaerobic processes over a given period of time on specific problems. For the moment we have proven that the optimal trajectory consists in approaching a unique singular arc as fast as possible when only one limiting substrate has to be converted, but the problem is still open when involving several substrates \cite{ghouali2012}. 
Another problem arises for alternating aerobic-anoxic systems. Revisiting the results obtained several years ago within the framework of Djalel Mazouni's thesis, we aims at proposing optimal time control policies for sequencing batch reactors in which simultaneous nitrification and denitrification take place. The solution for the original problem is a difficult task but we have already proposed a solution for a slightly modified model \cite{bouhafs2012}. These last results have been obtained within the framework of the PhD thesis of W. Bouhafs.

Reference points in batch processes can be mimicked by a series of continuously stirred bioreactors in series at steady state (see applications \ref{wine} and \ref{module.contracts.CAFE}). We study the minimal time problem to drive the nutrients concentrations of a cascade of chemostats. The control variable is the dilution rates of each tank, under the constraint that each dilution rate is bounded by the one of the previous tank, that makes the system not locally controllable. For the particular case of two tanks with total mass at steady state, the planar feedback synthesis has been found but the problem is still under investigation for the general case.


One important issue in bioprocesses is to find optimal feedback control laws in order to steer a system describing a perfectly-mixed bioreactor to a given target value in a minimal amount of time. Finding adequate feeding strategies can significantly  improve the performance of the system. A typical target (for fed-batch bioreactors) is to consider the substrate concentration to be lower than a given reference value at the end of the process. Other criterium can be studied  such as the maximization of the production of biomass in a given time period. Singular strategies (in reference to the theory of singular arcs in optimal control theory) can be defined in this context and are natural due to the constraints on the system. One objective of our research is to characterize optimal feedback control laws using mathematical tools from optimal control laws, and also to develop numerical methods that can handle problems with a large number of parameters. 




%......................................................................
\subsubsection{Modelling the functioning of soil ecosystems}
\label{section-modelsoils}
\begin{participants}
	\pers{C\'eline}{Casenave},
        \pers{J\'er\^ome}{Harmand},
	\pers{Alain}{Rapaport}
\end{participants}

In ecology, one of the important challenges is the understanding of the biodiversity observed in the natural ecosystems. Several models have been proposed to explain this biodiversity, and in particular the coexistence of different species. In these models, it is often assumed that, when they die, the micro-organisms are directly converted in an assimilable resource, that is a resource that alive organisms can consume. However, we know that it is not the case in reality. Indeed, the organic matter stemmed from the dead organisms has to be transformed in assimilable resource before it can be consumed. This transformation is performed by some micro-organisms which have this special ability.

   We  have proposed a new model of soil ecosystems, of chemostat type. This model is rather simple, but also original because it takes into account several mechanisms:
   \begin{itemize}
   \item the growth, the mortality and the respiration,
   \item the ability of some organisms to transform the non assimilable resources in assimilable ones,
   \item the advantage that an organism can gain from this ability of transformation.
   \end{itemize}
For the moment, we have considered the case where only one or two types of organisms are present. The model is finally composed of 3 (or 4) nonlinear ordinary differential equations: one per type of organisms, one for the assimilable resource and one for the non assimilable one.
The study of the equilibrium points has first shown the possibility of coexistence, at equilibrium, of the two organisms.
Then, in numerical simulations, we have observed the possible existence of limit cycles, which can also explain the coexistence of organisms observed in the nature.

This problem is still under study; a working group (in particular with
researchers of the UMR Eco \& Sols, conducted by B. Jaillard) meet regularly to discuss about
the problems of modelling in ecology.

We have also investigated the {\em sampling effect} that occurs when
micro-biologists select randomly species in a natural ecosystem
for studying reconstituted ecosystems in a controlled environment.
We have proposed a very simple probabilistic model, that shows that
observing average increases or decreases on the
performances of these reconstitute ecosystems when modifying the size
of the sampling, allows to infer kinds and proportions of the interactions
among species present in the original ecosystem \cite{jaillard2012}.
This research is conducted with the UMR Eco \& Sols, Montpellier,
(B. Jaillard) and the UMR BIOEMCO, Grignon (N. Nunan).


%......................................................................
\subsubsection{Equivalence between models of fractured porous media}
\label{section-fracturedmedia}
\begin{participants}
	\pers{C\'eline}{Casenave},
	\pers{J\'er\^ome}{Harmand},
	\pers{Alain}{Rapaport},
	\pers{Alejandro}{Rojas-Palma}
\end{participants}

In geosciences, models of fractured porous media are often described
as a {\em mobile} zone driven by advection, and one or several {\em
  immobile zones} directly or indirectly connected to the mobile zone by diffusion terms.
We believe that these models are also relevant to describe flows in
soil or in porous media such as biofilms. They are very close from
the spatial representations used in Section
\ref{section-bioremediation}.
We have shown, using a transfer function approach, that two schemes
often used in the literature: the MINC
(Multiple INteractive Continua) where diffusive compartments are
connected in series, and the
MRMT (Multiple Rate Mass Transfer) where diffusive compartments
are connected in star around the mobile zone, are equivalent input-output
representations \cite{rapportRojas2012}, and providing formulas (up to
three compartments) to pass from one representation to another.
This result means that one can simply choose the most convenient approach
when dealing with control or optimization without any loss of generality.
We are currently working on the general case of $n$ compartments with
$n$ larger than three, and looking
for equivalent classes of configurations that could be half way between
MINC and MRMT and fit better the spatial representations of real
world.

This work is performed with the UMR GéoSciences Rennes (J.R. de Dreuzy), and
has led to the internship of a Chilean MsC student (A. Rojas-Palma).




%......................................................................
\subsubsection{Non-linear filtering for the chemostat}

\begin{participants}
	\pers{Boumediene}{Benyahia},
	\pers{Amine}{Boutoub},
	\pers{Fabien}{Campillo},
	\pers{J\'er\^ome}{Harmand},
\end{participants}


Monte Carlo-based inference methods like particle filtering are bound to develop in the context of biotechnology. In contrast with the classical observer approach, inference through Monte Carlo methods can handle measurements in discrete time in low frequency and with low signal-to- noise ratio. Based on the stochastic modeling of the chemostat, these approaches may also be used for model selection and hypothesis testing. 

In a preliminary work \cite{benyahia2012a} we consider the bootstrap particle filter applied to a 2-dimensional chemostat model. The internship of Amine Boutoub dedicated to the study of particle filtering for more realistic chemostat models has recently started.




%......................................................................
\subsubsection{Functional identification of growth functions in the chemostat}
\label{section-functionalidentification}

\begin{participants}
	\pers{Alain}{Rapaport}
\end{participants}

We have proposed an adaptive control law that allows one to identify
    unstable steady states of the open-loop system in the
    single-species chemostat model without the knowledge of the
  growth function. We have then shown how to use a continuation technique to
  reconstruct the whole graph of the growth function, providing a new
  method for identifying non-monotonic growths \cite{sieber:hal-00723246,sieber2012}.
Two variants, in continuous and discrete time, have been studied.  An
analysis of the case of two
  species in competition has shown the ability of the method to detect
a mixed culture for which dominance depends on the dilution rate, due
to a property of stability loss in slow-fast dynamics.
This method leaves open future extensions for extremum seeking
problems.

This work has been conducted in cooperation with Universities of
Exeter (J. Sieber) and
Plymouth (S. Rodrigues), and the EPI SISYPHE (M. Desroches).


%......................................................................
\subsubsection{Diffusive representation of integro-differential models}
\label{section-Diffusive}

\begin{participants}
	\pers{C\'{e}line}{Casenave}
\end{participants}

This work is done in collaboration with Emmanuel Montseny (LAAS/CNRS), 
G\'{e}rard Montseny (LAAS/CNRS), and Christophe Prieur (LIAFA/CNRS).

In lots of dynamic systems of Physics or others scientific fields such as Biology (Volterra models), dynamic integral operators, often of convolution type, are involved. Problems relating to integro-differential models are often difficult to solve, especially because these models are not time-local. In this context, the methodology called “diffusive representation” presents some interests: an integral operator is represented by its gamma-symbol, directly deduced from its transfer function. It can be formulated by means of a state realization whose dimension is numerically reasonable whatever the size of the system may be. In addition to this interesting practical side, the diffusive representation offers a unified mathematical framework, well adapted to analysis of integral convolution operators.

Several dynamic problems can be tackled in an original and quite simple way by using the diffusive representation. In fact, all the operatorial problems of modeling, simulation, control, model identification, model reduction, etc. can be formulated in such a way that the object of the problem is the gamma-symbol of the operator solution.

Several problems are under study:
\begin{itemize}
\item the identification of integro-differential models \cite{casenave2012_1}, 
\item the controllability of some SISO Volterra models \cite{casenave2012_2}, 
\item the simulation and the analysis of a model of porous media\cite{casenave2012_3}.
\end{itemize}
These works follow up on the ones developed during the PhD thesis of C\'{e}line Casenave, which deals with the problem of the operator inversion for the application to non local dynamic problems. 
\end{module}
%----------------------------------------------------------------------





%---------------------------------------------------------------------

\begin{module}{resultats}{applications}{Applications}

%......................................................................
\subsubsection{Modelling and control of Anaerobic Digestion processes}
\label{SectionMBR}

\begin{participants}
	\pers{Boumediene}{Benyahia},
	\pers{Amine}{Charfi},
	\pers{Radhouene}{Fekih-Salem},
	\pers{J\'er\^ome}{Harmand},
        \pers{Guilherme}{Pimentel},
	\pers{Tewfik}{Sari}
\end{participants}


We consider the AM2 or AMOCO model developed in \footcite{Bernard2001} and extend both the model in itself
and its analysis to the following cases:
\begin{itemize}

\item Depending on the AM2 model parameters, the steady states were
analytically characterized and their stability were analyzed \cite{benyahia2012c}.
Following this study, it was shown that the overloading
tolerance, a parameter proposed in \footcite{Hess2007}
to on-line monitoring anaerobic processes, may be not adapted under
certain operating conditions and even lead to bad operating decisions.

\item Within the framework of the PhD theses of Amine Charfi and Boumediene Benyahia,
we have included the fouling dynamics of membranes into
the AM2 and we have analyzed
the resulting model (called the AM2b) \cite{charfi2012,benyahia2012b}.

\item We actually work towards two directions: (i) we are extending these results
in including into the AM2 an additional process, {\it i. e.} the hydrolysis step in order
to study bioprocesses treating solid waste (the resulting model being called the AM3) \cite{fekhi2012c,fekhi2012b}; (ii) we try to find
links between complex models such as the ADM1 model
and simple models such as the AM2b or the AM3 \cite{hassam2012}.
\end{itemize}

Apart from this work on the modelling of anaerobic digesters and membrane bioreactors,
 we have developed a number of 
specific simple models for control design accounting for the coupling of such processes with membrane modules
in the chemostat (PhD thesis of G. Pimentel). This work aims
at contributing to the efficient treatment of wastewaters produced in fish production
farms. The work of G. Pimentel aims at studying the coupling of simple fouling models
with the model of the chemostat in order to propose new simple models
for control design.

%......................................................................
\subsubsection{Hybrid modelling of biofilms in plug-flow reactors}
\label{sec.ibm.disco}

\begin{participants}
	\pers{Fabien}{Campillo},
	\pers{Chlo\' e}{Deygout},
	\pers{Annick}{Lesne},
	\pers{Alain}{Rapaport}
\end{participants}

We have proposed a multi-scaled modelling that combines three scales: a microscopic one for the individual bacteria, a mesoscopic or ``coarse-grained'' one
that homogenises at an intermediate scale the quantities relevant to the attachment/detachment process, and a macroscopic one in terms of substrate
concentration.

Such a ``hybrid'' approach allows for modelling and understanding in plug-flow reactors the interplay between
\begin{itemize}
\item the formation of the biofilm at a microscopic scale, that starts from a small number of bacteria (thus a stochastic individual based description),
\item  the limitation of the biofilm, due the carrying capacity of the wall attachment, at a mesoscopic scale,
\item  the consumption of nutrient along the flow at a macroscopic level, as a solution of a coupled transport-reaction partial differential equation.
\end{itemize}
The numerical computation of such a model requires a software
architecture that allows the simultaneous simulation of stochastic
events at the bacteria scale and the continuous evolution (in space and
time) of the substrate density.

This work has been conducted within the DISCO project
(see Section \ref{module.contrats.DISCO}) and the postdoctoral stay of
C. Deygout hired by the project, in close collaboration with A. Lesne
(LPTMC, Univ. Paris VI).
A first paper on the simulation model has been published \cite{deygout2013a}.

Within the DISCO project, experiments on real tubular plug-flow
reactors have been simultaneously driven at
IRSTEA Antony with the perspective of comparison with numerical
simulations.

The multi-species case with different bacteria specialized in
different environments (poor or rich in nutrient) is a work in
progress.

%......................................................................
\subsubsection{Individual-based models for the bacterial degradation of the cellulose}
\label{section.IBM.cellulose}

\begin{participants}
	\pers{Fabien}{Campillo},
	\pers{Chlo\' e}{Deygout}
\end{participants}

We propose an individual-based model for the degradation of one cellulose bead (dozens of micrometers in diameter) by cellulolytic bacteria. This model accounts for biofilm formation with minimal hypotheses: soluble substrate diffusion combined with bacterial chemotaxis-like movement in the liquid phase, lack of bacterial movement in the solid phase. The IBM results are qualitatively different from the main macroscopic degradation models previously used for cellulose degradation. It suggests that random and discrete processes could significantly impact the cellulose degradation dynamics by their effect on the spatial structuration of the colonized cellulose particles \cite{bize2012a}.



%......................................................................
\subsubsection{Modelling and control of cascade biosystems to mimic batch wine making processes}
\label{wine}

\begin{participants}
    \pers{Térence}{Bayen},
	\pers{C\'eline}{Casenave},
	\pers{J\'er\^ome}{Harmand},
	\pers{Alain}{Rapaport},
    \pers{Matthieu}{Sebbah}
\end{participants}

An experimental setup of four tanks connected in series has been designed by the research unit SPO (Montpellier) for studying four physiological stages of yeast as steady state.
The manipulated variables are the flow rates $Q_{i}$ of each tank with the constraint $Q_{i}\geq Q_{i-1}\geq 0$, and the objective is to reach simultaneously four set-points in the four tanks. We are studying two kinds of control strategies:
\begin{itemize}
\item a linearizing feedback law that drives exponentially the dynamics to the target. This is not the fastest strategy but is has good robustness properties. Nevertheless, the inputs constraint imposes to use saturation functions that provide satisfactory convergence in simulations but that is hard to prove mathematically.
\item a minimal time feedback. Due to lack of local controllability
  imposed by the constraint on the inputs, the optimal synthesis is
  not smooth with the presence of ``barriers''. The input constraint
  $Q_{i}\geq Q_{i-1}\geq 0$ is unusual in optimal control problems
  that are linear w.r.t. to the control. The optimality of
  candidate singular arcs is still open for this problem.
\end{itemize}
This summer, some experiments have been made to test the first feedback law on the experimental setup. The control law seems to perform work, but other experiments should be made next year with more reliable input flow pumps.

This work was conducted as a part of the European CAFE project (Computer-Aided Food processes for control Engineering) described in Section \ref{module.contracts.CAFE}.

%......................................................................
\subsubsection{Modelling and control of an ice cream crystallization process}
\label{icecream}

\begin{participants}
	\pers{C\'eline}{Casenave},
	\pers{Denis}{Dochain}
\end{participants}

In the ice cream industry, the type of final desired product (large cartons or ice creams on a stick) determine the viscosity at which the ice cream has to be produced. The control the viscosity of the ice cream at the outlet of a continuous crystallizer is therefore an important challenge.
The problem has been studied in two steps.
First, we have completed and validated on experimental data the reduced order model of the system. This model has been obtained by application of the method of moments on a population balance equation describing the evolution of the crystal size distribution.
Then, we have proposed a nonlinear control strategy to control of the viscosity of the ice cream with the temperature of the refrigerant fluid of the crystallizer. This control strategy is based on a linearizing control law coupled with a Smith predictor to account for the measurement delay. The control has been validated on an experimental pilot plant located at IRSTEA (Antony, France).

This work was conducted as a part of the European CAFE project
(Computer-Aided Food processes for control Engineering) described in
Section \ref{module.contracts.CAFE}.


%......................................................................
\subsubsection{Bioremediation of natural resources}
\label{section-bioremediation}
\begin{participants}
        \pers{Sébastien}{Barbier},
        \pers{J\'er\^ome}{Harmand},
	\pers{Alain}{Rapaport},
	\pers{Antoine}{Rousseau}
\end{participants}

The objective of this work is to provide efficient strategies for the
bioremediation of natural water resources. The originality of the approach is to
couple minimal time strategies that are determined on a simplified
model with a faithful numerical model for the hydrodynamics.
This work has been carried out in close cooperation with A. Rousseau.
Based on a previous paper that deals with an implicit representation of
the spatial inhomogeneity of the resource with a small number of homogeneous
compartments (with a system of ODEs), we have implemented a coupled ODE-PDE system that
accounts for the spatial non-homogeneity of pollution in natural resources. The
main idea is to implement a Navier-Stokes model in the resource (such as a lake),
with boundary conditions that correspond to the output feedback that has been
determined to be optimal for the simple ODEs model of a (small) bioreactor. A
first mathematical model has been introduced and numerical simulations have been
performed in academic situations.
During the internship of S. Barbier (co-advised by A. Rousseau and
A. Rapaport) we built a reduced model that approximates the reference PDE model
thanks to a set of ODEs with parameters. Numerical optimization is performed on
these parameters in order to better fit the reference model. This will lead to a
publication.

The study of the minimal time strategies on the system of ODEs has been mainly achieved in cooperation with Chilean researchers
(P. Gajardo, Universidad Tecnica  Federico Santa Maria, and H. Ramirez, Centro de Modelamiento Matemático) and a Chilean PhD student (V. Riquelme, Depto. Ingenieria Matematica, Universidad de Chile) within the
associated team DYMECOS \cite{rapportVictor2012}.

%......................................................................
\subsubsection{Modelling and simulating terrestrial plant ecological dynamics}
\label{sec.recent.ecological.dynamics}

\begin{participants}
	\pers{Fabien}{Campillo}
\end{participants}

This study is part of the ANR Syscomm MODECOL that is done in collaboration particularly with the University of Rennes I, the University of La Rochelle and INRIA. The first semester of 2012 was the last part of the project. We propose a very original individual-based model for clonal plant dynamics in continuous time and space that focuses on the effects of the network structure of the plants on the reproductive strategy of ramets. The model is coupled with a PDE dynamics for resources. The basic structure of the IBM encompass a population of ``ramets'' (the individuals) connected by ``stolons or rhizomes'' (the network)
\cite{campillo:hal-00723209,vangroenendael:hal-00717348}. See 
\url{http://www-sop.inria.fr/members/Fabien.Campillo/software/ibm-clonal/} for more details.



%......................................................................
\subsubsection{Modelling and inferring agricultural dynamics}
\label{sec.recent.agricultural.dynamics}
\begin{participants}
	\pers{Fabien}{Campillo},
	\pers{Angelo}{Raherinirina}
\end{participants}


The International Laboratory LIRMA supports this work that is done in
collaboration with the University of Fianarantsoa in Madagascar and
with Dominique Herv\'e (IRD, Fianarantsoa, Madagascar). The aim is to
study the dynamics of agricultural plots on the edge of primary
forest. In \cite{campillo2012d} a simple Markov model has been
successfully confronted to a first data set with the help of maximum
likelihood and Bayesian approaches. On a new data set developed by
IRD, the Markov hypothesis has been rejected and we proposed to use
semi-Makov models: for this new dataset the law of the sojourn time on
certain states will depend on the next state visited, which is
incompatible with the Markov hypothesis and which is consistent with
the semi-Markov hypothesis.



\end{module}
%---------------------------------------------------------------------




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Section contrats (Bilateral Contracts and Grants with Industry)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%----------------------------------------------------------------------
\begin{module}{contrats}{cafe}{CAFE}
\label{module.contracts.CAFE}
\begin{participants}
	\pers{C\'eline}{Casenave},
	\pers{J\'er\^ome}{Harmand},
 	\pers{Alain}{Rapaport}
\end{participants}


The objective of the CAFE European project is to provide new paradigms
for the smart control of food processes, on the basis of four typical processes in the areas of bioconversion,
separation, preservation and structuring, see details in \url{http://www.cafe-project.org}. The novelty of the project lies in the capacity of combining PAT
(Process Analytical Technology) and sensing devices with models and simulation environment with the
following objectives:
\begin{enumerate}
\item to extract as much as possible information from the process/plant in the form of precise estimations
of unmeasured variables defining, in particular, product quality, and of physical parameters changing
as the process dynamics does or difficult to know beforehand;

\item 
to save and encode the information in a reliable and usable way, basically via physical/deterministic
models;
\item
to develop control methods to keep uniform quality and production, despite the variability in the raw
material and/or to respond to sudden changes in the demand.
\end{enumerate}
MODEMIC is involved in the wine making supervision part (see
Section \ref{wine}) and in the ice cream crystallization control part (see Section \ref{icecream}).



\end{module}
%----------------------------------------------------------------------

%----------------------------------------------------------------------
\begin{module}{contrats}{dimimos}{DIMIMOS}
\begin{participants}
	\pers{J\'er\^ome}{Harmand},
	\pers{Alain}{Rapaport}
\end{participants}


DIMIMOS is an ANR SYSTERRA 2008 project of 4 years headed by the UMR Microbiologie du Sol et de l'Environnement (INRA Dijon).

This fundamental research project aims at better understanding the functional microbial soil ecosystems with
respect to the turnover of soil organic matter (SOM). More specifically, we aim at evaluating the role of the
microbial diversity in transforming SOM, in order to better manage the carbon in its biochemical global cycle
within agro-ecosystems. This project must deliver new insights for managing agricultural productivity (allow
better agricultural practices) while maintaining a high quality of
soil over the long term.

For the final stage of the project, the theoretical results obtained
in Section \ref{section-modelsoils} need to be confronted with the data provided by the partners.

\end{module}
%----------------------------------------------------------------------


%----------------------------------------------------------------------
\begin{module}{contrats}{disco}{DISCO}
\label{module.contrats.DISCO}
\begin{participants}
	\pers{Fabien}{Campillo},
	\pers{Chlo\' e}{Deygout},
	\pers{Bart}{Haegeman},
	\pers{J\'er\^ome}{Harmand},
        \pers{Annick}{Lesne},
	\pers{Claude}{Lobry},
	\pers{Alain}{Rapaport},
	\pers{Tewfik}{Sari}
\end{participants}

DISCO (Multi-scale modelling bioDIversity Structure COupling in
biofilms) is a three years project funded by the ANR SYSCOMM since the
end of 2009, that aims at developing and studying computational and
mathematical models of biofilm dynamics, taking into account the
biodiversity (distribution of bacteria species) and spatial
structure; see details in \url{https://sites.google.com/site/anrdisco/}.

Several ``go back'' between simulation models and experiments in
plug-flow reactors performed at IRSTEA Antony have been conducted
during the two postdoctoral years of C. Deygout hired by the project.
A first paper on the simulation of a multi-scale model has been published \cite{deygout2013a}
and a second one on the confrontation with experiments is in
preparation (see Section \ref{sec.ibm.disco}).


At a macro-scale, the team has studied several extensions of the
chemostat model dedicated to microbial ecosystems with biofilm
(see Section \ref{theory_chemostat} and the publication
\cite{fekih2013}).

A new collaboration has been launched with the HBAN team at IRSTEA
Antony, within this project, about the modelling of cellulose
degradation. Cellulose is typically available in small balls (but ten
times larger than the average size of microorganisms) that are first
converted by enzymatic activity into carbon substrate that can then be
assimilated by the microorganisms. Some of the microorganisms are
attached to these balls, creating a particular aggregates structure.

An IBM for the degradation of one cellulose bead (dozens of micrometers in diameter) by cellulolytic bacteria has been developed. Our aim is to determine the macroscopic degradation behavior. The initial stages of the degradation process may involve a very limited number of bacteria that cannot be properly modelled by classical models based on deterministic equations (see Section \ref{section.IBM.cellulose} and communications \cite{bize2012a} and \cite{bize2012b}).

The duration of the project has been extended by the ANR to May
2013, in order for the team to prepare a final restitution
at Paris in spring 2013.

\end{module}
%----------------------------------------------------------------------


%----------------------------------------------------------------------
\begin{module}{contrats}{modecol}{MODECOL}
\label{module.contrats.modecol}
\begin{participants}
	\pers{Fabien}{Campillo}
\end{participants}



The ANR SYSCOMM Project MODECOL (January 2009/June 2012) involves three INRIA project-teams (MODEMIC, MAESTRO and TOSCA) with the UMR Ecobio (Ecosystèmes, Biodiversité, Evolution, Rennes), the University of La Rochelle and the Universities of Houston and Berkeley. The aim of the INRIA component  is to propose individual-based models for terrestrial prairial plant
communities' dynamics in the context of water purifying from nitrate and pesticides. 
The results of the INRIA component have been published  \cite{campillo:hal-00723209}
This year was also dedicated to the edition of a special issue of Ecological Modelling on ``Modelling clonal plant growth'' \cite{vangroenendael:hal-00717348}. See 
\url{http://www-sop.inria.fr/members/Fabien.Campillo/software/ibm-clonal/} for more details.


\end{module}
%----------------------------------------------------------------------



%----------------------------------------------------------------------



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Section partenariat (Partnerships and Cooperations)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%----------------------------------------------------------------------
%%% Dans cette section, certains modules sont **normalises**.
%%% Par consequent, la liste de ces modules
%%% est :
%%%
%%% \begin{module}{partenariat}{regional}{Regional Initiatives}
%%% \begin{module}{partenariat}{national}{National Initiatives}
%%% \begin{module}{partenariat}{europe}{European Initiatives}
%%% \begin{module}{partenariat}{international}{International Initiatives}
%%% \begin{module}{partenariat}{visites}{International Research Visitors}
%%%
%%% On peut, en outre, ajouter des modules pour inserer ce qui ne
%%% rentre pas dans les categories ci-dessus. Pour chacun des modules
%%% listes, les actions proprement dites apparaitront en
%%% \subsubsection, et les listes de {participants} seront ventilees en
%%% consequence, par \subsubsection (et non plus par module)
%----------------------------------------------------------------------



%---------------------------------------------------------------------
%\begin{module}{partenariat}{regional}{Regional Initiatives}
%
%\end{module}
%---------------------------------------------------------------------


%%---------------------------------------------------------------------
%\begin{module}{partenariat}{national}{National Initiatives}
%
%%.....................................................................
%\subsection{ANR}
%
%%.....................................................................
%\subsection{Competitivity Clusters}
%
%\end{module}
%%---------------------------------------------------------------------

%%----------------------------------------------------------------------
%\begin{module}{partenariat}{europe}{European Initiatives}
%
%\subsection{FP7 Projects}
%xxx
%
%\subsection{Collaborations in European Programs, except FP7}
%xxx
%% respecter le format
%\begin{itemize}
%\XMLaddatt*{type}{sanspuces}
%	\item Program:
%	\item Project acronym:
%	\item Project title:
%	\item Duration: mois ann\'ee d\'ebut - mois ann\'ee fin
%	\item Coordinator:
%	\item Other partners: organisme, labo (pays)
%	\item Abstract:
%\end{itemize}
%
%\subsection{Collaborations with Major European Organizations}
%
%% respecter le format
% \begin{itemize}
% \XMLaddatt*{type}{sanspuces}
%        \item Partner 1: organisme 1, labo 1 (pays 1)
%        \item Sujet 1 (max. 2 lignes)
% \end{itemize}
% \begin{itemize}
% \XMLaddatt*{type}{sanspuces}
%       \item Partner 2: organisme 2, labo 2 (pays 2)
%       \item Sujet 2 (max. 2 lignes)
% \end{itemize}
%
%
%\end{module}
%%----------------------------------------------------------------------


%%---------------------------------------------------------------------
%\begin{module}{international}{international}{International Initiatives}
%
%
%
%
%
%\end{module}
%%----------------------------------------------------------------------








%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
%%% Information sur les données importées : équipes associées et autres actions internationales
%%%
%%% La rubrique est pré-remplie avec les 3 items suivants issus
%%% de la base de la Direction des Relations Internationales (DRI):
%%% Si vous voyez des erreurs, signalez-les \`a raweb-support@inria.fr.
%%%
%%% - Inria Associate Teams
%%%
%%% - Inria International Partners
%%%
%%% - Participation in other International Programs :
%%%
%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




%----------------------------------------------------------------------
\begin{module}{partenariat}{internationalInitiatives}{International Initiatives}

%......................................................................
\subsection{INRIA Associate Teams}



%.....................................................................
\subsubsection{Associated team DYMECOS}
\label{dymecos}

\begin{participants}
    \pers{Térence}{Bayen},
	\pers{Fabien}{Campillo},
	\pers{J\'er\^ome}{Harmand},
	\pers{Claude}{Lobry},
	\pers{Alain}{Rapaport},
    \pers{Alejandro}{Rojas-Palma},
	\pers{Tewfik}{Sari},
	\pers{Matthieu}{Sebbah}
\end{participants}

\begin{itemize}
\XMLaddatt*{type}{sanspuces}
\item Program: \href{http://www.inria.fr/en/research/international-mobility/associate-teams/programme}{Associate Teams}
 \item Title: DYnamical Microbial and Environmental eCOSystems
 \item INRIA principal investigator: Alain Rapaport
 \item International Partners (Institution -  Laboratory - Researcher):
 \begin{itemize}
    \XMLaddatt*{type}{sanspuces}
    \item Universidad de Chile /
          Departamento de Ingeniería Matemática
          - Universidad de Chile / CNRS (Chile)
           / Centro de Modelamiento Matemático (CMM)
           - Héctor Ram\`\i rez
    \item Universidad Tecnica  Federico Santa Maria (Chile)
           - Departamento de Matematica
           - Pedro Gajardo
 \end{itemize}
 \item Duration: 01/01/2010 - 31/12/2012
 \item
DYMECOS is an associated team with Chile, mainly with CMM (Centro de Modelamiento Matem\'atico), Univ. de Chile, Santiago, DIM
(Departamento de Ingenier{\'\i}a Matem\'atica), Universidad de Chile, Santiago and Departamento de Matematica, Universidad Tecnica Federico Santa Maria (UTFSM).

Two kinds of investigations have been conducted:
\begin{itemize}
\item minimal time control problems of fedbatch processes with several species, and optimal strategies for the bioremediation of natural water resources,
\item stochastic modelling of the chemostat.
\end{itemize}

The second Franco-Chilean Workshop on Bioprocess Modelling has been
co-organized by the team and the Chilean partners in January at
Puc\'on (see
  \url{https://sites.google.com/site/eadymecos/evenements}).
The workshop gathers mathematicians, process engineers and
micro-biologists.

C. Lobry, A. Rapaport and T. Sari have participated to the 3rd LAWOC
(Latin American Workshop on Optimization and Control) held in
Valparaiso, Chile \cite{lobryLAWOC2012,rapaportLAWOC2012,Sari14}.


This year, the team has received A. Rojas-Palma as a MSc Internship for 3
months, and M. Sebbah has been hired by INRIA-CIRIC for a postdoctoral
stay of 3 months in the team (Oct.-Nov. 2012) followed by 13 months in
Chile (starting Jan. 2013).

\end{itemize}





%......................................................................
\subsection{INRIA International Partners}
% indique un partenariat international important pour votre équipe,
% hors Equipes Associées et hors participation aux programmes
% internationaux mentionnés ci-dessous

%......................................................................
\subsection{Participation In International Programs}
%participation aux differents programmes
%%%    * implication dans les activités des laboratoires conjoints \`a l'étranger (CIRIC Chili,
%%%		JLPC Etats-Unis ; LIRIMA Afrique ; JFLI Japon ; LIAMA Chine)
%%%    * participation aux différents programmes soutenus par la DRI et/ou des financeurs externes
%%%	  (Euromediterranée 3+3, STIC Algérie, STIC Tunisie, STIC AmSud, Math AmSud, Inria-CNPq, Inria-FAPs,
%%%  Inria-CONICyT, Inria-MINCyT, Reussi USA, Inria@SILICONVALLEY, STIC Asie, Inria-Russie, Autres)

%........................

\subsubsection{CIRIC-Bionature}

The team has contributed to the writing proposal of the Bionature
line of the CIRIC (Communication and Information Research and
Innovation Center) in Chile.

The 16 months postdoctoral grant of M. Sebbah (3 months in France, 13
months in Chile) is supported by INRIA-Chile within this research
program (see Section \ref{dymecos}).

\subsubsection{TREASURE}
\begin{participants}
	\pers{Fabien}{Campillo},
	\pers{J\'er\^ome}{Harmand},
	\pers{Claude}{Lobry},
	\pers{Tewfik}{Sari}
\end{participants}

\begin{itemize}
\XMLaddatt*{type}{sanspuces}
\item Program: \href{http://www.inria.fr/en/institute/international-relations/international-calls-for-projects/euromediterranean-3-3}{Euromediterranean 3+3}
 \item Title: Treatment and Sustainable Reuse of Effluents in semiarid climates
 \item INRIA principal investigator: Jérôme HARMAND
 \item International Partners (Institution -  Laboratory - Researcher):
 \begin{itemize}
    \XMLaddatt*{type}{sanspuces}
    \item University of santiago de compostella (Spain)
 - Environmental engineering -  Juan  GARRIDO
    \item National Research Center (Egypt)
 - Water Pollution Control -  Helmy  EL-ZANFALY
    \item Université Française d'Egypte (Egypt)
 - mathematiques -  Mohamed  JAOUA
    \item Institut National de la Recherche Agronomique (France)
 - dpts EA, MICA et MIA -  Pascal  NEVEU
    \item University of Tlemcen (Algeria)
 - Automatic control -  Brahim  CHERKI
    \item University of Patras (Greece)
 - Process Control Laboratory -  Costas  KRAVARIS
    \item Centre de Biotechnology de Sfax (Tunisia)
 - Department of environmental engineering -  Sami  SAYADI
    \item Université Cadi Ayyad de Marrakech -Faculté des Sciences de Semlalia - Dépt. de Mathématiques (Morocco)
 - Centre National de Recherche sur l'Eau et l'Energie -  Laila  MANDI
    \item Ecole Nationale des Ingénieurs de Tunis (Tunisia)
 - Mathématiques -  Nabil  GMATI
 \end{itemize}
 \item The TREASURE network aims at integrating knowledge on the modelling, the control and the optimization of biological systems for the treatment and reuse of wastewaters in countries submitted to semi-arid climates under both socio-economical and agronomic constraints within the actual context of global changes. A special focus of the actual project concerns the integration of technical skills together with socio-economical and agronomic studies for the integrated solutions developed within the network to be evaluated and tested in practice in the partner's countries and, as possible as it may be within the context of the actual research network, valorizing these proposed technologies with the help of industrial on site in parters from South.
\end{itemize}


%.............................................
\subsubsection{LIRIMA Stic-Mada}
\begin{participants}
	\pers{Fabien}{Campillo},
	\pers{Angelo}{Raherinirina}
\end{participants}

\begin{itemize}
\XMLaddatt*{type}{sanspuces}
\item Program: \href{http://www.inria.fr/institut/relations-internationales/appels-a-projets/lirima}{LIRIMA}
 \item Title: Stic-Madagascar
 \item INRIA principal investigator: Fabien Campillo
 \item International Partners (Institution -  Laboratory - Researcher):
 \begin{itemize}
    \XMLaddatt*{type}{sanspuces}
    \item University of Antananarivo (Madagascar)  - Lala Andriamampianina
    \item University of Fianarantsoa  (Madagascar) - Rivo Rakotozafy
 \end{itemize}
 \item The MODEMIC Project-Team is coordinator of the LIRIMA/Stic-Mada project for the theme: modelling and management of natural resources. In 2012, Angelo Raherinirina (co-advised with F. Campillo and R. Rakotozafy) made a 6 months stay in MODEMIC team-project, he will defend his thesis in January 2013 (see Section \ref{sec.recent.agricultural.dynamics}). 
 
 
\end{itemize}



\end{module}
%---------------------------------------------------------------------


%---------------------------------------------------------------------
\begin{module}{partenariat}{internationalVisitors}{International Research Visitors}
% http://intranet.inria.fr/disc/publier/raweb2012instructions.html#Visitors


%-------------------
\subsection{Visits of International Scientists}
%chercheurs invites, profs invites (via universite), Les internships
%sont a mettre dans la subsection suivante.
D. Dochain, from CESAME, Univ. Louvain-la-Neuve (Belgium), has spent
one month in the team. D. Dochain is the coordinator of the CAFE
project (see Section \ref{module.contracts.CAFE}).


%-------------------
\subsubsection {Internships}
A. Rojas-Palma, MSc student at Univ. of Chile, has spent 3 months in
the team, in the scope of the INRIA Internships (see Section \ref{dymecos}).


%-------------------
\subsection{Visits to International Teams}
%(nom, date, univ ou labo de destination) : les sejours Sabbatiques, les sejours Explorateurs
% les sejours de chercheurs d'une durée superieure a un mois, dans une université ou un laboratoire étranger

B. Haegeman is on secondment to CNRS since September 2012.  He is working
at the Centre of Biodiversity Theory and Modelling which is part of the
Station for Experimental Ecology in Moulis (Ari\`ege).


\end{module}
%---------------------------------------------------------------------







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
%%% Section diffusion des resultats
%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




%---------------------------------------------------------------------
\begin{module}{diffusion}{animation}{Animation of the scientific community}

\begin{itemize}

\item A. Rapaport is presently the head of the UMR INRA-SupAgro MISTEA (Mathematics, Informatics and STatistics for Environment and Agronomy) where the team is housed. A. Rapaport is:
member of the piloting board of the ``modelling'' axis of the LabEx Numev (Digital and Hardware Solutions, Modelling for the Environment and Life Sciences)) at Montpellier; member of the scientific board of the ``Ecotechnologies'' department of IRSTEA; member of the scientific board of the ``BIOS'' department of CIRAD.
A. Rapaport has been the president of the AERES visiting committee of
  the Research team ``MOTIVE'' of IRSTEA.

\item F. Campillo is member of the NICE (long term invited scientists selection); deputy elected member of the INRIA Scientific Council; member of the internal communication working group of INRIA Sophia Antipolis. F. Campillo was member of the INRA selection board for the selection of junior scientists (statistics and modelling).

\item J. Harmand is the responsible for the treasure-2 network (a 3+3 Euromed project) that has been accepted for funding for the next 4 years);
member of the scientific council of the Environment and agronomic
INRA department; member of the advisory board of the INRA metaprogram MEM (Meta-omic and Microbial Ecosystems); member
of the INRA evaluation commission STEA (``Sciences de la Terre, de l'eau et de l'atmosphère''). J. Harmand is member of the steering committee of the MEM INRA metaprogram.
  J. Harmand is member of the scientific committee of the INRA Environment and Agronomy department.

\item J. Harmand and A. Rapaport are responsible of the INRA network
  MODYM (MOd\`eles DYnamiques et M\'etabolites) sponsored by the
  Applied Mathematics and Informatics Departement (MIA) of INRA.

\item B. Haegeman is Academic Editor for PLoS ONE.


\end{itemize}

\end{module}
%---------------------------------------------------------------------

%---------------------------------------------------------------------
\begin{module}{diffusion}{seminars}{Seminars and schools}

The MODEMIC project-team animates several seminars:
\begin{itemize}

\item The MODEMIC seminar on mathematical modelling [\href{http://www-sop.inria.fr/modemic/seminaire/}{http://www-sop.inria.fr/modemic/seminaire/}].

\item  I3M and MODEMIC working group on stochastic models for ecology and biology [\href{http://www-sop.inria.fr/modemic/personnel/campillo/GT-modelisation.html}{http://www-sop.inria.fr/modemic/personnel/campillo/GT-modelisation.html}]; this working group is supported by the  ``laboratory of excellence'' (LabEx) \href{http://www2.lirmm.fr/numev/}{NUMEV} (Digital and Hardware Solutions, Modelling for the Environment and Life Sciences).

\item A new seminar SAMOCOD on Optimisation, Control and Dynamics
  bilocated at Montpellier and Avignon will be launched in January
  2013
  [\href{http://ens.math.univ-montp2.fr/SPIP/sem.php3?a=programme&sem=618}{http://ens.math.univ-montp2.fr/SPIP/sem.php3?a=programme&sem=61}]. A. Rapaport
  is member of the organizing committee.

\end{itemize}

\end{module}
%---------------------------------------------------------------------


%---------------------------------------------------------------------
\begin{module}{diffusion}{enseignement}{Teaching}

\begin{itemize}


\item F. Campillo and M. Joannides have given a 20 hours lecture on ``Stochastic modelling of ecosystems'' at the Master 2 in Biostatistics in Universit\'e de Montpellier II.


\item A. Rapaport has given a 25 hours lecture on differential equations with applications in the ``Practical Mathematics'' module for 1st year students in MSc in Mathematics at University Montpellier II.

\item C. Casenave, F. Campillo, J. Harmand and A. Rapaport are in
  charge of two modules in the new MSc program ``STIC - Environnement'' at
University Montpellier II:
\begin{itemize}
\item Introduction to mathematical modelling, master I (50 hours)
\item Advanced mathematical modelling, master II (75 hours)
\end{itemize}

\item C. Casenave, F. Campillo and A. Rapaport have delivered a 20 hours doctoral module at University Montpellier II, entitled ``Modelling for biology and ecology -- mathematical and computational methods''.

\item A. Rapaport and T. Bayen have given six lectures on mathematical modelling for 1st year students of SupAgro Montpellier.

\item A. Rapaport has given two lectures on Modelling and numerical simulations at the ``EcoSyst\`emes'' Master at University of Montpellier II.


\end{itemize}

\end{module}
%---------------------------------------------------------------------




%---------------------------------------------------------------------
\begin{module}{diffusion}{encadrement}{PhD's}

Defended thesis:
\begin{itemize}

\item
Boumediène Benyahia, ``Mod\'elisation et contr\^ole de bior\'eacteurs \`a membrane'';
grant: Coadvise and Treasure;
thesis in co-supervision Montpellier-Tlemcen (Algeria);
started in October 2008;
advisors: J. Harmand and B. Cherki (Tlemcen, Algeria).

		
\end{itemize}

Theses in progress:
\begin{itemize}

%\item HdR : nom du chercheur, titre du m\'emoire, nom de l'Universit\'e, date de soutenance


\item Mamadou Lamine Diagne, ``Mod\'elisation math\'ematique du Typha'';
grant: AUF;
thesis in co-supervision Mulhouse-Saint Louis (Senegal);
started in October 2009;
advisors: T. Sari and M.T Niane (Saint Louis, Senegal).

\item
Radhouene Fekih-Salem, ``La compétition et la coexistence dans le Chemostat'';
grant: Averroes;
thesis in co-supervision Montpellier-Tunis;
started in October 2010;
advisors: A. Rapaport, T. Sari and N. Gmati (Tunis).


\item
Walid Bouhafs, ``Commande optimale des réacteurs séquentiels discontinus'';
grant: Université Tunis Carthage;
thesis in co-supervision Montpellier-Tunis;
started in October 2010;
advisors: J. Harmand,  F. Jean (ENSTA-ParisTech, Paris) and Nahla Abdellatif (Tunis, Tunisia).

     
\item
Amel Ghouali, ``control en tamps minimal des réacteurs de digestion anaérobie'';
grant: Averroes;
thesis in co-supervision Montpellier-Tlemcen (Algeria);
started in October 2011;
advisors: J. Harmand and A. Moussaoui  (Tlemcen, Algeria).

\item
Sonia Hassam, ``Réduction de modèles de la digestion anaérobie'';
grant: Univ. Tlemcen;
started in October 2010;
advisors: J. Harmand and B. Cherki  (Tlemcen, Algeria).

\item Angelo Raherinirina, ``Mod\'elisation markovienne de dynamique d'usage des sols'';
grant: AUF, SCAC Madagascar, LIRIMA;
started March 1st 2009;
advisors: F. Campillo and R. Rakotozafy (Univ. Fianarantsoa Madagascar).

\item Coralie Fritsch, ``Simulation et analyse de mod\`eles individu-centr\'es d'\'ecosyst\`emes bact\'eriens pour des proc\'ed\'es biotechnologiques'', \'ecole doctorale I2S;
grant: INRA Metaprogram MEM and Univ. Montpellier II;
started October 1st 2011;
advisors: F. Campillo, J. Harmand.


\item Guilherme Pimentel, ``Modelling and control of bioreactors with membrane'';
grant: Univ. Mons (Belgium) and INRA;
thesis in co-supervision Montpellier-Mons;
started October 2011;
advisors: A. Rapaport, J. Harmand and A. VandeWouver (Univ. Mons).

\item Amine Charfi, ``Mod\'elisation du colmatage dans les r\'eacteurs  \`a membranes''
grant: Coadvise and University of Tunis;
started October 2009;
advisors: J. Harmand and Nihel Benamar.


\end{itemize}

\end{module}
%---------------------------------------------------------------------


%---------------------------------------------------------------------
\begin{module}{diffusion}{committees}{Participation to thesis committees}

\begin{itemize}


\item F. Campillo (referee): M. Jean-Louis Marchand, ``Conditionnement de processus markoviens'', Univ. de Rennes 1.

\item F. Campillo (referee): M. Quentin Molto, ``Estimation de
  biomasse en for\^et tropicale humide Propagation des incertitudes dans
  la mod\'elisation de la distribution spatiale de la biomasse en Guyane
  fran\c caise'', Univ. des Antilles et de la Guyane.

\item J. Harmand (referee): M. Thomas Guélon, ``Déterminer l'influence de la distribution spatiale des bactéries sur les propriétés 
microscopiques de biofilms bactériens par des techniques d'homogénéisation'', Univ. Blaise Pascal, Clermont II.

\item J. Harmand, T. Sari, C. Lobry (president of the committee): 
M. Boumediene, ``Modélisation et observation
des bioprocédés à membranes : application à la digestion anaérobie'', Univ. Montpellier 2 and Univ. Tlemcen, Algérie.


\item A. Rapaport (president of the committee): M. Sebbah, ``Stabilité d'inégalités
  variationnelles et prox-régularité, équations de Kolmogorov
  périodiques contrôlées'' , Univ. Montpellier II.

\item A. Rapaport (referee and president of the committee): Léontine Nkague Nkamba,
``Robustesse des seuils en épidémiologie et stabilité asymptotique
d'un modèle \`a infectivité et susceptibilité différentielle'',
Univ. Metz and Univ. St-Louis du Sénégal.

\item C. Lobry (president of the committee): Jonathan Rault ``Modélisation structurée en taille du zooplancton'' UNSA.

\end{itemize}

\end{module}
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%% MODEMIC
%% Date : mardi 4 décembre 2012, 21:52:22 (UTC+0100)
%% Source rapport latex MODEMIC : http://ralyx.inria.fr/Raweb/modemic/uid0.html
%% Source donnees bastri SR0486QR : https://bastri.inria.fr/Bastri/structureinria/siid/SR0486QR/look
%% Source donnees bil MODEMIC : https://bil.inria.fr/
